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3.31
Integrals 3001 to 3078
3.31.1
\(\int \genfrac {}{}{}{}{(d x)^m}{\sqrt {a+\genfrac {}{}{}{}{b}{\sqrt {\genfrac {}{}{}{}{c}{x}}}}} \, dx\) [3001]
3.31.2
\(\int \genfrac {}{}{}{}{(d x)^m}{\sqrt {a+\genfrac {}{}{}{}{b}{(\genfrac {}{}{}{}{c}{x})^{3/2}}}} \, dx\) [3002]
3.31.3
\(\int (a+b (c x^n)^{\genfrac {}{}{}{}{1}{n}}) \, dx\) [3003]
3.31.4
\(\int (a+b (c x^n)^{\genfrac {}{}{}{}{1}{n}})^2 \, dx\) [3004]
3.31.5
\(\int (a+b (c x^n)^{\genfrac {}{}{}{}{1}{n}})^3 \, dx\) [3005]
3.31.6
\(\int \genfrac {}{}{}{}{x^3}{a+b (c x^n)^{\genfrac {}{}{}{}{1}{n}}} \, dx\) [3006]
3.31.7
\(\int \genfrac {}{}{}{}{x^2}{a+b (c x^n)^{\genfrac {}{}{}{}{1}{n}}} \, dx\) [3007]
3.31.8
\(\int \genfrac {}{}{}{}{x}{a+b (c x^n)^{\genfrac {}{}{}{}{1}{n}}} \, dx\) [3008]
3.31.9
\(\int \genfrac {}{}{}{}{1}{a+b (c x^n)^{\genfrac {}{}{}{}{1}{n}}} \, dx\) [3009]
3.31.10
\(\int \genfrac {}{}{}{}{1}{x (a+b (c x^n)^{\genfrac {}{}{}{}{1}{n}})} \, dx\) [3010]
3.31.11
\(\int \genfrac {}{}{}{}{1}{x^2 (a+b (c x^n)^{\genfrac {}{}{}{}{1}{n}})} \, dx\) [3011]
3.31.12
\(\int \genfrac {}{}{}{}{1}{x^3 (a+b (c x^n)^{\genfrac {}{}{}{}{1}{n}})} \, dx\) [3012]
3.31.13
\(\int \genfrac {}{}{}{}{x^3}{(a+b (c x^n)^{\genfrac {}{}{}{}{1}{n}})^2} \, dx\) [3013]
3.31.14
\(\int \genfrac {}{}{}{}{x^2}{(a+b (c x^n)^{\genfrac {}{}{}{}{1}{n}})^2} \, dx\) [3014]
3.31.15
\(\int \genfrac {}{}{}{}{x}{(a+b (c x^n)^{\genfrac {}{}{}{}{1}{n}})^2} \, dx\) [3015]
3.31.16
\(\int \genfrac {}{}{}{}{1}{(a+b (c x^n)^{\genfrac {}{}{}{}{1}{n}})^2} \, dx\) [3016]
3.31.17
\(\int \genfrac {}{}{}{}{1}{x (a+b (c x^n)^{\genfrac {}{}{}{}{1}{n}})^2} \, dx\) [3017]
3.31.18
\(\int \genfrac {}{}{}{}{1}{x^2 (a+b (c x^n)^{\genfrac {}{}{}{}{1}{n}})^2} \, dx\) [3018]
3.31.19
\(\int \genfrac {}{}{}{}{1}{x^3 (a+b (c x^n)^{\genfrac {}{}{}{}{1}{n}})^2} \, dx\) [3019]
3.31.20
\(\int \genfrac {}{}{}{}{1}{(a+b (c x^n)^{\genfrac {}{}{}{}{1}{n}})^3} \, dx\) [3020]
3.31.21
\(\int \genfrac {}{}{}{}{x}{(1+(x^n)^{\genfrac {}{}{}{}{1}{n}})^2} \, dx\) [3021]
3.31.22
\(\int x^3 (a+b (c x^n)^{\genfrac {}{}{}{}{1}{n}})^p \, dx\) [3022]
3.31.23
\(\int x^2 (a+b (c x^n)^{\genfrac {}{}{}{}{1}{n}})^p \, dx\) [3023]
3.31.24
\(\int x (a+b (c x^n)^{\genfrac {}{}{}{}{1}{n}})^p \, dx\) [3024]
3.31.25
\(\int (a+b (c x^n)^{\genfrac {}{}{}{}{1}{n}})^p \, dx\) [3025]
3.31.26
\(\int \genfrac {}{}{}{}{(a+b (c x^n)^{\genfrac {}{}{}{}{1}{n}})^p}{x} \, dx\) [3026]
3.31.27
\(\int \genfrac {}{}{}{}{(a+b (c x^n)^{\genfrac {}{}{}{}{1}{n}})^p}{x^2} \, dx\) [3027]
3.31.28
\(\int (a+b (c x^n)^{2/n})^3 \, dx\) [3028]
3.31.29
\(\int (a+b (c x^n)^{2/n})^2 \, dx\) [3029]
3.31.30
\(\int (a+b (c x^n)^{2/n}) \, dx\) [3030]
3.31.31
\(\int \genfrac {}{}{}{}{1}{a+b (c x^n)^{2/n}} \, dx\) [3031]
3.31.32
\(\int \genfrac {}{}{}{}{1}{(a+b (c x^n)^{2/n})^2} \, dx\) [3032]
3.31.33
\(\int \genfrac {}{}{}{}{1}{(a+b (c x^n)^{2/n})^3} \, dx\) [3033]
3.31.34
\(\int \genfrac {}{}{}{}{1}{1+4 \sqrt {x^4}} \, dx\) [3034]
3.31.35
\(\int \genfrac {}{}{}{}{1}{1-4 \sqrt {x^4}} \, dx\) [3035]
3.31.36
\(\int \genfrac {}{}{}{}{1}{1+4 \sqrt [3]{x^6}} \, dx\) [3036]
3.31.37
\(\int \genfrac {}{}{}{}{1}{1-4 \sqrt [3]{x^6}} \, dx\) [3037]
3.31.38
\(\int \genfrac {}{}{}{}{1}{1+4 (x^{2 n})^{\genfrac {}{}{}{}{1}{n}}} \, dx\) [3038]
3.31.39
\(\int \genfrac {}{}{}{}{1}{1-4 (x^{2 n})^{\genfrac {}{}{}{}{1}{n}}} \, dx\) [3039]
3.31.40
\(\int (a+b (c x^n)^{3/n})^3 \, dx\) [3040]
3.31.41
\(\int (a+b (c x^n)^{3/n})^2 \, dx\) [3041]
3.31.42
\(\int (a+b (c x^n)^{3/n}) \, dx\) [3042]
3.31.43
\(\int \genfrac {}{}{}{}{1}{a+b (c x^n)^{3/n}} \, dx\) [3043]
3.31.44
\(\int \genfrac {}{}{}{}{1}{(a+b (c x^n)^{3/n})^2} \, dx\) [3044]
3.31.45
\(\int \genfrac {}{}{}{}{1}{(a+b (c x^n)^{3/n})^3} \, dx\) [3045]
3.31.46
\(\int (d x)^m (a+b (c x^q)^n)^p \, dx\) [3046]
3.31.47
\(\int x^2 (a+b (c x^q)^n)^p \, dx\) [3047]
3.31.48
\(\int x (a+b (c x^q)^n)^p \, dx\) [3048]
3.31.49
\(\int (a+b (c x^q)^n)^p \, dx\) [3049]
3.31.50
\(\int \genfrac {}{}{}{}{(a+b (c x^q)^n)^p}{x} \, dx\) [3050]
3.31.51
\(\int \genfrac {}{}{}{}{(a+b (c x^q)^n)^p}{x^2} \, dx\) [3051]
3.31.52
\(\int \sqrt {a+b \sqrt {\genfrac {}{}{}{}{d}{x}}+\genfrac {}{}{}{}{c}{x}} x^m \, dx\) [3052]
3.31.53
\(\int \sqrt {a+b \sqrt {\genfrac {}{}{}{}{d}{x}}+\genfrac {}{}{}{}{c}{x}} x^2 \, dx\) [3053]
3.31.54
\(\int \sqrt {a+b \sqrt {\genfrac {}{}{}{}{d}{x}}+\genfrac {}{}{}{}{c}{x}} x \, dx\) [3054]
3.31.55
\(\int \sqrt {a+b \sqrt {\genfrac {}{}{}{}{d}{x}}+\genfrac {}{}{}{}{c}{x}} \, dx\) [3055]
3.31.56
\(\int \genfrac {}{}{}{}{\sqrt {a+b \sqrt {\genfrac {}{}{}{}{d}{x}}+\genfrac {}{}{}{}{c}{x}}}{x} \, dx\) [3056]
3.31.57
\(\int \genfrac {}{}{}{}{\sqrt {a+b \sqrt {\genfrac {}{}{}{}{d}{x}}+\genfrac {}{}{}{}{c}{x}}}{x^2} \, dx\) [3057]
3.31.58
\(\int \genfrac {}{}{}{}{\sqrt {a+b \sqrt {\genfrac {}{}{}{}{d}{x}}+\genfrac {}{}{}{}{c}{x}}}{x^3} \, dx\) [3058]
3.31.59
\(\int \genfrac {}{}{}{}{\sqrt {a+b \sqrt {\genfrac {}{}{}{}{d}{x}}+\genfrac {}{}{}{}{c}{x}}}{x^4} \, dx\) [3059]
3.31.60
\(\int \genfrac {}{}{}{}{x^m}{\sqrt {a+b \sqrt {\genfrac {}{}{}{}{d}{x}}+\genfrac {}{}{}{}{c}{x}}} \, dx\) [3060]
3.31.61
\(\int \genfrac {}{}{}{}{x^2}{\sqrt {a+b \sqrt {\genfrac {}{}{}{}{d}{x}}+\genfrac {}{}{}{}{c}{x}}} \, dx\) [3061]
3.31.62
\(\int \genfrac {}{}{}{}{x}{\sqrt {a+b \sqrt {\genfrac {}{}{}{}{d}{x}}+\genfrac {}{}{}{}{c}{x}}} \, dx\) [3062]
3.31.63
\(\int \genfrac {}{}{}{}{1}{\sqrt {a+b \sqrt {\genfrac {}{}{}{}{d}{x}}+\genfrac {}{}{}{}{c}{x}}} \, dx\) [3063]
3.31.64
\(\int \genfrac {}{}{}{}{1}{\sqrt {a+b \sqrt {\genfrac {}{}{}{}{d}{x}}+\genfrac {}{}{}{}{c}{x}} x} \, dx\) [3064]
3.31.65
\(\int \genfrac {}{}{}{}{1}{\sqrt {a+b \sqrt {\genfrac {}{}{}{}{d}{x}}+\genfrac {}{}{}{}{c}{x}} x^2} \, dx\) [3065]
3.31.66
\(\int \genfrac {}{}{}{}{1}{\sqrt {a+b \sqrt {\genfrac {}{}{}{}{d}{x}}+\genfrac {}{}{}{}{c}{x}} x^3} \, dx\) [3066]
3.31.67
\(\int \genfrac {}{}{}{}{1}{\sqrt {a+b \sqrt {\genfrac {}{}{}{}{d}{x}}+\genfrac {}{}{}{}{c}{x}} x^4} \, dx\) [3067]
3.31.68
\(\int \sqrt {\sqrt {\genfrac {}{}{}{}{1}{x}}+\genfrac {}{}{}{}{1}{x}} \, dx\) [3068]
3.31.69
\(\int \sqrt {2+\sqrt {\genfrac {}{}{}{}{1}{x}}+\genfrac {}{}{}{}{1}{x}} \, dx\) [3069]
3.31.70
\(\int (c x^n)^{\genfrac {}{}{}{}{1}{n}} (a+b (c x^n)^{\genfrac {}{}{}{}{1}{n}})^p \, dx\) [3070]
3.31.71
\(\int (c x^n)^{\genfrac {}{}{}{}{1}{n}} (a+b (c x^n)^{\genfrac {}{}{}{}{1}{n}})^3 \, dx\) [3071]
3.31.72
\(\int (c x^n)^{\genfrac {}{}{}{}{1}{n}} (a+b (c x^n)^{\genfrac {}{}{}{}{1}{n}})^2 \, dx\) [3072]
3.31.73
\(\int (c x^n)^{\genfrac {}{}{}{}{1}{n}} (a+b (c x^n)^{\genfrac {}{}{}{}{1}{n}}) \, dx\) [3073]
3.31.74
\(\int \genfrac {}{}{}{}{(c x^n)^{\genfrac {}{}{}{}{1}{n}}}{a+b (c x^n)^{\genfrac {}{}{}{}{1}{n}}} \, dx\) [3074]
3.31.75
\(\int \genfrac {}{}{}{}{(c x^n)^{\genfrac {}{}{}{}{1}{n}}}{(a+b (c x^n)^{\genfrac {}{}{}{}{1}{n}})^2} \, dx\) [3075]
3.31.76
\(\int \genfrac {}{}{}{}{(c x^n)^{\genfrac {}{}{}{}{1}{n}}}{(a+b (c x^n)^{\genfrac {}{}{}{}{1}{n}})^3} \, dx\) [3076]
3.31.77
\(\int \genfrac {}{}{}{}{(c x^n)^{\genfrac {}{}{}{}{1}{n}}}{(a+b (c x^n)^{\genfrac {}{}{}{}{1}{n}})^4} \, dx\) [3077]
3.31.78
\(\int \genfrac {}{}{}{}{(c x^n)^{\genfrac {}{}{}{}{1}{n}}}{(a+b (c x^n)^{\genfrac {}{}{}{}{1}{n}})^5} \, dx\) [3078]
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