Optimal. Leaf size=1254 \[ -\frac {\sqrt {a-b+c} \tan ^{-1}\left (\frac {\sqrt {a-b+c} \tan (d+e x)}{\sqrt {c \tan ^4(d+e x)+b \tan ^2(d+e x)+a}}\right )}{2 e}+\frac {\tan (d+e x) \sqrt {c \tan ^4(d+e x)+b \tan ^2(d+e x)+a}}{3 e}-\frac {\sqrt {c} \tan (d+e x) \sqrt {c \tan ^4(d+e x)+b \tan ^2(d+e x)+a}}{e \left (\sqrt {c} \tan ^2(d+e x)+\sqrt {a}\right )}+\frac {b \tan (d+e x) \sqrt {c \tan ^4(d+e x)+b \tan ^2(d+e x)+a}}{3 \sqrt {c} e \left (\sqrt {c} \tan ^2(d+e x)+\sqrt {a}\right )}+\frac {\sqrt [4]{a} \sqrt [4]{c} E\left (2 \tan ^{-1}\left (\frac {\sqrt [4]{c} \tan (d+e x)}{\sqrt [4]{a}}\right )|\frac {1}{4} \left (2-\frac {b}{\sqrt {a} \sqrt {c}}\right )\right ) \left (\sqrt {c} \tan ^2(d+e x)+\sqrt {a}\right ) \sqrt {\frac {c \tan ^4(d+e x)+b \tan ^2(d+e x)+a}{\left (\sqrt {c} \tan ^2(d+e x)+\sqrt {a}\right )^2}}}{e \sqrt {c \tan ^4(d+e x)+b \tan ^2(d+e x)+a}}-\frac {\sqrt [4]{a} b E\left (2 \tan ^{-1}\left (\frac {\sqrt [4]{c} \tan (d+e x)}{\sqrt [4]{a}}\right )|\frac {1}{4} \left (2-\frac {b}{\sqrt {a} \sqrt {c}}\right )\right ) \left (\sqrt {c} \tan ^2(d+e x)+\sqrt {a}\right ) \sqrt {\frac {c \tan ^4(d+e x)+b \tan ^2(d+e x)+a}{\left (\sqrt {c} \tan ^2(d+e x)+\sqrt {a}\right )^2}}}{3 c^{3/4} e \sqrt {c \tan ^4(d+e x)+b \tan ^2(d+e x)+a}}+\frac {\sqrt [4]{c} (a-b+c) F\left (2 \tan ^{-1}\left (\frac {\sqrt [4]{c} \tan (d+e x)}{\sqrt [4]{a}}\right )|\frac {1}{4} \left (2-\frac {b}{\sqrt {a} \sqrt {c}}\right )\right ) \left (\sqrt {c} \tan ^2(d+e x)+\sqrt {a}\right ) \sqrt {\frac {c \tan ^4(d+e x)+b \tan ^2(d+e x)+a}{\left (\sqrt {c} \tan ^2(d+e x)+\sqrt {a}\right )^2}}}{2 \sqrt [4]{a} \left (\sqrt {a}-\sqrt {c}\right ) e \sqrt {c \tan ^4(d+e x)+b \tan ^2(d+e x)+a}}-\frac {\left (b-c+\sqrt {a} \sqrt {c}\right ) F\left (2 \tan ^{-1}\left (\frac {\sqrt [4]{c} \tan (d+e x)}{\sqrt [4]{a}}\right )|\frac {1}{4} \left (2-\frac {b}{\sqrt {a} \sqrt {c}}\right )\right ) \left (\sqrt {c} \tan ^2(d+e x)+\sqrt {a}\right ) \sqrt {\frac {c \tan ^4(d+e x)+b \tan ^2(d+e x)+a}{\left (\sqrt {c} \tan ^2(d+e x)+\sqrt {a}\right )^2}}}{2 \sqrt [4]{a} \sqrt [4]{c} e \sqrt {c \tan ^4(d+e x)+b \tan ^2(d+e x)+a}}+\frac {\sqrt [4]{a} \left (b+2 \sqrt {a} \sqrt {c}\right ) F\left (2 \tan ^{-1}\left (\frac {\sqrt [4]{c} \tan (d+e x)}{\sqrt [4]{a}}\right )|\frac {1}{4} \left (2-\frac {b}{\sqrt {a} \sqrt {c}}\right )\right ) \left (\sqrt {c} \tan ^2(d+e x)+\sqrt {a}\right ) \sqrt {\frac {c \tan ^4(d+e x)+b \tan ^2(d+e x)+a}{\left (\sqrt {c} \tan ^2(d+e x)+\sqrt {a}\right )^2}}}{6 c^{3/4} e \sqrt {c \tan ^4(d+e x)+b \tan ^2(d+e x)+a}}-\frac {\left (\sqrt {a}+\sqrt {c}\right ) (a-b+c) \Pi \left (-\frac {\left (\sqrt {a}-\sqrt {c}\right )^2}{4 \sqrt {a} \sqrt {c}};2 \tan ^{-1}\left (\frac {\sqrt [4]{c} \tan (d+e x)}{\sqrt [4]{a}}\right )|\frac {1}{4} \left (2-\frac {b}{\sqrt {a} \sqrt {c}}\right )\right ) \left (\sqrt {c} \tan ^2(d+e x)+\sqrt {a}\right ) \sqrt {\frac {c \tan ^4(d+e x)+b \tan ^2(d+e x)+a}{\left (\sqrt {c} \tan ^2(d+e x)+\sqrt {a}\right )^2}}}{4 \sqrt [4]{a} \left (\sqrt {a}-\sqrt {c}\right ) \sqrt [4]{c} e \sqrt {c \tan ^4(d+e x)+b \tan ^2(d+e x)+a}} \]
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Rubi [A] time = 0.99, antiderivative size = 1254, normalized size of antiderivative = 1.00, number of steps used = 14, number of rules used = 9, integrand size = 35, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.257, Rules used = {3700, 1335, 1091, 1197, 1103, 1195, 1208, 1216, 1706} \[ -\frac {\sqrt {a-b+c} \tan ^{-1}\left (\frac {\sqrt {a-b+c} \tan (d+e x)}{\sqrt {c \tan ^4(d+e x)+b \tan ^2(d+e x)+a}}\right )}{2 e}+\frac {\tan (d+e x) \sqrt {c \tan ^4(d+e x)+b \tan ^2(d+e x)+a}}{3 e}-\frac {\sqrt {c} \tan (d+e x) \sqrt {c \tan ^4(d+e x)+b \tan ^2(d+e x)+a}}{e \left (\sqrt {c} \tan ^2(d+e x)+\sqrt {a}\right )}+\frac {b \tan (d+e x) \sqrt {c \tan ^4(d+e x)+b \tan ^2(d+e x)+a}}{3 \sqrt {c} e \left (\sqrt {c} \tan ^2(d+e x)+\sqrt {a}\right )}+\frac {\sqrt [4]{a} \sqrt [4]{c} E\left (2 \tan ^{-1}\left (\frac {\sqrt [4]{c} \tan (d+e x)}{\sqrt [4]{a}}\right )|\frac {1}{4} \left (2-\frac {b}{\sqrt {a} \sqrt {c}}\right )\right ) \left (\sqrt {c} \tan ^2(d+e x)+\sqrt {a}\right ) \sqrt {\frac {c \tan ^4(d+e x)+b \tan ^2(d+e x)+a}{\left (\sqrt {c} \tan ^2(d+e x)+\sqrt {a}\right )^2}}}{e \sqrt {c \tan ^4(d+e x)+b \tan ^2(d+e x)+a}}-\frac {\sqrt [4]{a} b E\left (2 \tan ^{-1}\left (\frac {\sqrt [4]{c} \tan (d+e x)}{\sqrt [4]{a}}\right )|\frac {1}{4} \left (2-\frac {b}{\sqrt {a} \sqrt {c}}\right )\right ) \left (\sqrt {c} \tan ^2(d+e x)+\sqrt {a}\right ) \sqrt {\frac {c \tan ^4(d+e x)+b \tan ^2(d+e x)+a}{\left (\sqrt {c} \tan ^2(d+e x)+\sqrt {a}\right )^2}}}{3 c^{3/4} e \sqrt {c \tan ^4(d+e x)+b \tan ^2(d+e x)+a}}+\frac {\sqrt [4]{c} (a-b+c) F\left (2 \tan ^{-1}\left (\frac {\sqrt [4]{c} \tan (d+e x)}{\sqrt [4]{a}}\right )|\frac {1}{4} \left (2-\frac {b}{\sqrt {a} \sqrt {c}}\right )\right ) \left (\sqrt {c} \tan ^2(d+e x)+\sqrt {a}\right ) \sqrt {\frac {c \tan ^4(d+e x)+b \tan ^2(d+e x)+a}{\left (\sqrt {c} \tan ^2(d+e x)+\sqrt {a}\right )^2}}}{2 \sqrt [4]{a} \left (\sqrt {a}-\sqrt {c}\right ) e \sqrt {c \tan ^4(d+e x)+b \tan ^2(d+e x)+a}}-\frac {\left (b-c+\sqrt {a} \sqrt {c}\right ) F\left (2 \tan ^{-1}\left (\frac {\sqrt [4]{c} \tan (d+e x)}{\sqrt [4]{a}}\right )|\frac {1}{4} \left (2-\frac {b}{\sqrt {a} \sqrt {c}}\right )\right ) \left (\sqrt {c} \tan ^2(d+e x)+\sqrt {a}\right ) \sqrt {\frac {c \tan ^4(d+e x)+b \tan ^2(d+e x)+a}{\left (\sqrt {c} \tan ^2(d+e x)+\sqrt {a}\right )^2}}}{2 \sqrt [4]{a} \sqrt [4]{c} e \sqrt {c \tan ^4(d+e x)+b \tan ^2(d+e x)+a}}+\frac {\sqrt [4]{a} \left (b+2 \sqrt {a} \sqrt {c}\right ) F\left (2 \tan ^{-1}\left (\frac {\sqrt [4]{c} \tan (d+e x)}{\sqrt [4]{a}}\right )|\frac {1}{4} \left (2-\frac {b}{\sqrt {a} \sqrt {c}}\right )\right ) \left (\sqrt {c} \tan ^2(d+e x)+\sqrt {a}\right ) \sqrt {\frac {c \tan ^4(d+e x)+b \tan ^2(d+e x)+a}{\left (\sqrt {c} \tan ^2(d+e x)+\sqrt {a}\right )^2}}}{6 c^{3/4} e \sqrt {c \tan ^4(d+e x)+b \tan ^2(d+e x)+a}}-\frac {\left (\sqrt {a}+\sqrt {c}\right ) (a-b+c) \Pi \left (-\frac {\left (\sqrt {a}-\sqrt {c}\right )^2}{4 \sqrt {a} \sqrt {c}};2 \tan ^{-1}\left (\frac {\sqrt [4]{c} \tan (d+e x)}{\sqrt [4]{a}}\right )|\frac {1}{4} \left (2-\frac {b}{\sqrt {a} \sqrt {c}}\right )\right ) \left (\sqrt {c} \tan ^2(d+e x)+\sqrt {a}\right ) \sqrt {\frac {c \tan ^4(d+e x)+b \tan ^2(d+e x)+a}{\left (\sqrt {c} \tan ^2(d+e x)+\sqrt {a}\right )^2}}}{4 \sqrt [4]{a} \left (\sqrt {a}-\sqrt {c}\right ) \sqrt [4]{c} e \sqrt {c \tan ^4(d+e x)+b \tan ^2(d+e x)+a}} \]
Antiderivative was successfully verified.
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Rule 1091
Rule 1103
Rule 1195
Rule 1197
Rule 1208
Rule 1216
Rule 1335
Rule 1706
Rule 3700
Rubi steps
\begin {align*} \int \tan ^2(d+e x) \sqrt {a+b \tan ^2(d+e x)+c \tan ^4(d+e x)} \, dx &=\frac {\operatorname {Subst}\left (\int \frac {x^2 \sqrt {a+b x^2+c x^4}}{1+x^2} \, dx,x,\tan (d+e x)\right )}{e}\\ &=\frac {\operatorname {Subst}\left (\int \left (\sqrt {a+b x^2+c x^4}-\frac {\sqrt {a+b x^2+c x^4}}{1+x^2}\right ) \, dx,x,\tan (d+e x)\right )}{e}\\ &=\frac {\operatorname {Subst}\left (\int \sqrt {a+b x^2+c x^4} \, dx,x,\tan (d+e x)\right )}{e}-\frac {\operatorname {Subst}\left (\int \frac {\sqrt {a+b x^2+c x^4}}{1+x^2} \, dx,x,\tan (d+e x)\right )}{e}\\ &=\frac {\tan (d+e x) \sqrt {a+b \tan ^2(d+e x)+c \tan ^4(d+e x)}}{3 e}+\frac {\operatorname {Subst}\left (\int \frac {2 a+b x^2}{\sqrt {a+b x^2+c x^4}} \, dx,x,\tan (d+e x)\right )}{3 e}+\frac {\operatorname {Subst}\left (\int \frac {-b+c-c x^2}{\sqrt {a+b x^2+c x^4}} \, dx,x,\tan (d+e x)\right )}{e}-\frac {(a-b+c) \operatorname {Subst}\left (\int \frac {1}{\left (1+x^2\right ) \sqrt {a+b x^2+c x^4}} \, dx,x,\tan (d+e x)\right )}{e}\\ &=\frac {\tan (d+e x) \sqrt {a+b \tan ^2(d+e x)+c \tan ^4(d+e x)}}{3 e}+\frac {\left (\sqrt {a} \left (2 \sqrt {a}+\frac {b}{\sqrt {c}}\right )\right ) \operatorname {Subst}\left (\int \frac {1}{\sqrt {a+b x^2+c x^4}} \, dx,x,\tan (d+e x)\right )}{3 e}-\frac {\left (b+\sqrt {a} \sqrt {c}-c\right ) \operatorname {Subst}\left (\int \frac {1}{\sqrt {a+b x^2+c x^4}} \, dx,x,\tan (d+e x)\right )}{e}-\frac {\left (\sqrt {a} b\right ) \operatorname {Subst}\left (\int \frac {1-\frac {\sqrt {c} x^2}{\sqrt {a}}}{\sqrt {a+b x^2+c x^4}} \, dx,x,\tan (d+e x)\right )}{3 \sqrt {c} e}+\frac {\left (\sqrt {a} \sqrt {c}\right ) \operatorname {Subst}\left (\int \frac {1-\frac {\sqrt {c} x^2}{\sqrt {a}}}{\sqrt {a+b x^2+c x^4}} \, dx,x,\tan (d+e x)\right )}{e}-\frac {\left (\sqrt {a} (a-b+c)\right ) \operatorname {Subst}\left (\int \frac {1+\frac {\sqrt {c} x^2}{\sqrt {a}}}{\left (1+x^2\right ) \sqrt {a+b x^2+c x^4}} \, dx,x,\tan (d+e x)\right )}{\left (\sqrt {a}-\sqrt {c}\right ) e}+\frac {\left (\sqrt {c} (a-b+c)\right ) \operatorname {Subst}\left (\int \frac {1}{\sqrt {a+b x^2+c x^4}} \, dx,x,\tan (d+e x)\right )}{\left (\sqrt {a}-\sqrt {c}\right ) e}\\ &=-\frac {\sqrt {a-b+c} \tan ^{-1}\left (\frac {\sqrt {a-b+c} \tan (d+e x)}{\sqrt {a+b \tan ^2(d+e x)+c \tan ^4(d+e x)}}\right )}{2 e}+\frac {\tan (d+e x) \sqrt {a+b \tan ^2(d+e x)+c \tan ^4(d+e x)}}{3 e}+\frac {b \tan (d+e x) \sqrt {a+b \tan ^2(d+e x)+c \tan ^4(d+e x)}}{3 \sqrt {c} e \left (\sqrt {a}+\sqrt {c} \tan ^2(d+e x)\right )}-\frac {\sqrt {c} \tan (d+e x) \sqrt {a+b \tan ^2(d+e x)+c \tan ^4(d+e x)}}{e \left (\sqrt {a}+\sqrt {c} \tan ^2(d+e x)\right )}-\frac {\sqrt [4]{a} b E\left (2 \tan ^{-1}\left (\frac {\sqrt [4]{c} \tan (d+e x)}{\sqrt [4]{a}}\right )|\frac {1}{4} \left (2-\frac {b}{\sqrt {a} \sqrt {c}}\right )\right ) \left (\sqrt {a}+\sqrt {c} \tan ^2(d+e x)\right ) \sqrt {\frac {a+b \tan ^2(d+e x)+c \tan ^4(d+e x)}{\left (\sqrt {a}+\sqrt {c} \tan ^2(d+e x)\right )^2}}}{3 c^{3/4} e \sqrt {a+b \tan ^2(d+e x)+c \tan ^4(d+e x)}}+\frac {\sqrt [4]{a} \sqrt [4]{c} E\left (2 \tan ^{-1}\left (\frac {\sqrt [4]{c} \tan (d+e x)}{\sqrt [4]{a}}\right )|\frac {1}{4} \left (2-\frac {b}{\sqrt {a} \sqrt {c}}\right )\right ) \left (\sqrt {a}+\sqrt {c} \tan ^2(d+e x)\right ) \sqrt {\frac {a+b \tan ^2(d+e x)+c \tan ^4(d+e x)}{\left (\sqrt {a}+\sqrt {c} \tan ^2(d+e x)\right )^2}}}{e \sqrt {a+b \tan ^2(d+e x)+c \tan ^4(d+e x)}}+\frac {\sqrt [4]{a} \left (b+2 \sqrt {a} \sqrt {c}\right ) F\left (2 \tan ^{-1}\left (\frac {\sqrt [4]{c} \tan (d+e x)}{\sqrt [4]{a}}\right )|\frac {1}{4} \left (2-\frac {b}{\sqrt {a} \sqrt {c}}\right )\right ) \left (\sqrt {a}+\sqrt {c} \tan ^2(d+e x)\right ) \sqrt {\frac {a+b \tan ^2(d+e x)+c \tan ^4(d+e x)}{\left (\sqrt {a}+\sqrt {c} \tan ^2(d+e x)\right )^2}}}{6 c^{3/4} e \sqrt {a+b \tan ^2(d+e x)+c \tan ^4(d+e x)}}-\frac {\left (b+\sqrt {a} \sqrt {c}-c\right ) F\left (2 \tan ^{-1}\left (\frac {\sqrt [4]{c} \tan (d+e x)}{\sqrt [4]{a}}\right )|\frac {1}{4} \left (2-\frac {b}{\sqrt {a} \sqrt {c}}\right )\right ) \left (\sqrt {a}+\sqrt {c} \tan ^2(d+e x)\right ) \sqrt {\frac {a+b \tan ^2(d+e x)+c \tan ^4(d+e x)}{\left (\sqrt {a}+\sqrt {c} \tan ^2(d+e x)\right )^2}}}{2 \sqrt [4]{a} \sqrt [4]{c} e \sqrt {a+b \tan ^2(d+e x)+c \tan ^4(d+e x)}}+\frac {\sqrt [4]{c} (a-b+c) F\left (2 \tan ^{-1}\left (\frac {\sqrt [4]{c} \tan (d+e x)}{\sqrt [4]{a}}\right )|\frac {1}{4} \left (2-\frac {b}{\sqrt {a} \sqrt {c}}\right )\right ) \left (\sqrt {a}+\sqrt {c} \tan ^2(d+e x)\right ) \sqrt {\frac {a+b \tan ^2(d+e x)+c \tan ^4(d+e x)}{\left (\sqrt {a}+\sqrt {c} \tan ^2(d+e x)\right )^2}}}{2 \sqrt [4]{a} \left (\sqrt {a}-\sqrt {c}\right ) e \sqrt {a+b \tan ^2(d+e x)+c \tan ^4(d+e x)}}-\frac {\left (\sqrt {a}+\sqrt {c}\right ) (a-b+c) \Pi \left (-\frac {\left (\sqrt {a}-\sqrt {c}\right )^2}{4 \sqrt {a} \sqrt {c}};2 \tan ^{-1}\left (\frac {\sqrt [4]{c} \tan (d+e x)}{\sqrt [4]{a}}\right )|\frac {1}{4} \left (2-\frac {b}{\sqrt {a} \sqrt {c}}\right )\right ) \left (\sqrt {a}+\sqrt {c} \tan ^2(d+e x)\right ) \sqrt {\frac {a+b \tan ^2(d+e x)+c \tan ^4(d+e x)}{\left (\sqrt {a}+\sqrt {c} \tan ^2(d+e x)\right )^2}}}{4 \sqrt [4]{a} \left (\sqrt {a}-\sqrt {c}\right ) \sqrt [4]{c} e \sqrt {a+b \tan ^2(d+e x)+c \tan ^4(d+e x)}}\\ \end {align*}
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Mathematica [C] time = 29.61, size = 639, normalized size = 0.51 \[ \frac {\sqrt {\frac {4 a \cos (2 (d+e x))+a \cos (4 (d+e x))+3 a-b \cos (4 (d+e x))+b-4 c \cos (2 (d+e x))+c \cos (4 (d+e x))+3 c}{4 \cos (2 (d+e x))+\cos (4 (d+e x))+3}} \left (\frac {(b-3 c) \sin (2 (d+e x))}{6 c}+\frac {1}{3} \tan (d+e x)\right )}{e}+\frac {-\frac {4 (b-3 c) \tan (d+e x) \left (a+b \tan ^2(d+e x)+c \tan ^4(d+e x)\right )}{\tan ^2(d+e x)+1}+\frac {i \sqrt {2} \sqrt {\frac {\sqrt {b^2-4 a c}+b+2 c \tan ^2(d+e x)}{\sqrt {b^2-4 a c}+b}} \sqrt {\frac {2 c \tan ^2(d+e x)}{b-\sqrt {b^2-4 a c}}+1} \left (\left (-b \left (\sqrt {b^2-4 a c}-3 c\right )+c \left (3 \sqrt {b^2-4 a c}-4 a-6 c\right )+b^2\right ) F\left (i \sinh ^{-1}\left (\sqrt {2} \sqrt {\frac {c}{b+\sqrt {b^2-4 a c}}} \tan (d+e x)\right )|\frac {b+\sqrt {b^2-4 a c}}{b-\sqrt {b^2-4 a c}}\right )+(b-3 c) \left (\sqrt {b^2-4 a c}-b\right ) E\left (i \sinh ^{-1}\left (\sqrt {2} \sqrt {\frac {c}{b+\sqrt {b^2-4 a c}}} \tan (d+e x)\right )|\frac {b+\sqrt {b^2-4 a c}}{b-\sqrt {b^2-4 a c}}\right )+6 c (a-b+c) \Pi \left (\frac {b+\sqrt {b^2-4 a c}}{2 c};i \sinh ^{-1}\left (\sqrt {2} \sqrt {\frac {c}{b+\sqrt {b^2-4 a c}}} \tan (d+e x)\right )|\frac {b+\sqrt {b^2-4 a c}}{b-\sqrt {b^2-4 a c}}\right )\right )}{\sqrt {\frac {c}{\sqrt {b^2-4 a c}+b}}}}{12 c e \sqrt {a+b \tan ^2(d+e x)+c \tan ^4(d+e x)}} \]
Warning: Unable to verify antiderivative.
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fricas [F] time = 1.67, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\sqrt {c \tan \left (e x + d\right )^{4} + b \tan \left (e x + d\right )^{2} + a} \tan \left (e x + d\right )^{2}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \[ \text {Timed out} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.42, size = 1945, normalized size = 1.55 \[ \text {result too large to display} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \sqrt {c \tan \left (e x + d\right )^{4} + b \tan \left (e x + d\right )^{2} + a} \tan \left (e x + d\right )^{2}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [F] time = 0.00, size = -1, normalized size = -0.00 \[ \int {\mathrm {tan}\left (d+e\,x\right )}^2\,\sqrt {c\,{\mathrm {tan}\left (d+e\,x\right )}^4+b\,{\mathrm {tan}\left (d+e\,x\right )}^2+a} \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \sqrt {a + b \tan ^{2}{\left (d + e x \right )} + c \tan ^{4}{\left (d + e x \right )}} \tan ^{2}{\left (d + e x \right )}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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