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]