3.5 Integrals 401 to 500

\(\int e^{\text {arctanh}(x)} x (1+x)^2 \, dx\) [401]
\(\int e^{\text {arctanh}(x)} (1+x)^2 \, dx\) [402]
\(\int \genfrac {}{}{}{}{e^{\text {arctanh}(x)} x}{1+x} \, dx\) [403]
\(\int \genfrac {}{}{}{}{e^{\text {arctanh}(x)}}{1+x} \, dx\) [404]
\(\int \genfrac {}{}{}{}{e^{\text {arctanh}(x)} x}{(1+x)^2} \, dx\) [405]
\(\int \genfrac {}{}{}{}{e^{\text {arctanh}(x)}}{(1+x)^2} \, dx\) [406]
\(\int e^{\text {arctanh}(a x)} x^2 \sqrt {c-a c x} \, dx\) [407]
\(\int e^{\text {arctanh}(a x)} x \sqrt {c-a c x} \, dx\) [408]
\(\int e^{\text {arctanh}(a x)} \sqrt {c-a c x} \, dx\) [409]
\(\int \genfrac {}{}{}{}{e^{\text {arctanh}(a x)} \sqrt {c-a c x}}{x} \, dx\) [410]
\(\int \genfrac {}{}{}{}{e^{\text {arctanh}(a x)} \sqrt {c-a c x}}{x^2} \, dx\) [411]
\(\int e^{2 \text {arctanh}(a x)} x^3 \sqrt {c-a c x} \, dx\) [412]
\(\int e^{2 \text {arctanh}(a x)} x^2 \sqrt {c-a c x} \, dx\) [413]
\(\int e^{2 \text {arctanh}(a x)} x \sqrt {c-a c x} \, dx\) [414]
\(\int e^{2 \text {arctanh}(a x)} \sqrt {c-a c x} \, dx\) [415]
\(\int \genfrac {}{}{}{}{e^{2 \text {arctanh}(a x)} \sqrt {c-a c x}}{x} \, dx\) [416]
\(\int \genfrac {}{}{}{}{e^{2 \text {arctanh}(a x)} \sqrt {c-a c x}}{x^2} \, dx\) [417]
\(\int \genfrac {}{}{}{}{e^{2 \text {arctanh}(a x)} \sqrt {c-a c x}}{x^3} \, dx\) [418]
\(\int \genfrac {}{}{}{}{e^{2 \text {arctanh}(a x)} \sqrt {c-a c x}}{x^4} \, dx\) [419]
\(\int \genfrac {}{}{}{}{e^{2 \text {arctanh}(a x)} \sqrt {c-a c x}}{x^5} \, dx\) [420]
\(\int e^{3 \text {arctanh}(a x)} x^3 \sqrt {c-a c x} \, dx\) [421]
\(\int e^{3 \text {arctanh}(a x)} x^2 \sqrt {c-a c x} \, dx\) [422]
\(\int e^{3 \text {arctanh}(a x)} x \sqrt {c-a c x} \, dx\) [423]
\(\int e^{3 \text {arctanh}(a x)} \sqrt {c-a c x} \, dx\) [424]
\(\int \genfrac {}{}{}{}{e^{3 \text {arctanh}(a x)} \sqrt {c-a c x}}{x} \, dx\) [425]
\(\int \genfrac {}{}{}{}{e^{3 \text {arctanh}(a x)} \sqrt {c-a c x}}{x^2} \, dx\) [426]
\(\int \genfrac {}{}{}{}{e^{3 \text {arctanh}(a x)} \sqrt {c-a c x}}{x^3} \, dx\) [427]
\(\int \genfrac {}{}{}{}{e^{3 \text {arctanh}(a x)} \sqrt {c-a c x}}{x^4} \, dx\) [428]
\(\int \genfrac {}{}{}{}{e^{3 \text {arctanh}(a x)} \sqrt {c-a c x}}{x^5} \, dx\) [429]
\(\int e^{\text {arctanh}(x)} x \sqrt {1+x} \, dx\) [430]
\(\int e^{\text {arctanh}(x)} \sqrt {1+x} \, dx\) [431]
\(\int e^{\text {arctanh}(x)} \sqrt {1-x} x \, dx\) [432]
\(\int e^{\text {arctanh}(x)} \sqrt {1-x} \, dx\) [433]
\(\int e^{\text {arctanh}(x)} x (1+x)^{3/2} \, dx\) [434]
\(\int e^{\text {arctanh}(x)} (1+x)^{3/2} \, dx\) [435]
\(\int e^{\text {arctanh}(x)} (1-x)^{3/2} x \, dx\) [436]
\(\int e^{\text {arctanh}(x)} (1-x)^{3/2} \, dx\) [437]
\(\int \genfrac {}{}{}{}{e^{\text {arctanh}(x)} x}{\sqrt {1+x}} \, dx\) [438]
\(\int \genfrac {}{}{}{}{e^{\text {arctanh}(x)}}{\sqrt {1+x}} \, dx\) [439]
\(\int \genfrac {}{}{}{}{e^{\text {arctanh}(x)} x}{\sqrt {1-x}} \, dx\) [440]
\(\int \genfrac {}{}{}{}{e^{\text {arctanh}(x)}}{\sqrt {1-x}} \, dx\) [441]
\(\int \genfrac {}{}{}{}{e^{\text {arctanh}(x)} x}{(1+x)^{3/2}} \, dx\) [442]
\(\int \genfrac {}{}{}{}{e^{\text {arctanh}(x)}}{(1+x)^{3/2}} \, dx\) [443]
\(\int \genfrac {}{}{}{}{e^{\text {arctanh}(x)} x}{(1-x)^{3/2}} \, dx\) [444]
\(\int \genfrac {}{}{}{}{e^{\text {arctanh}(x)}}{(1-x)^{3/2}} \, dx\) [445]
\(\int e^{-\text {arctanh}(a x)} x^2 \sqrt {c-a c x} \, dx\) [446]
\(\int e^{-\text {arctanh}(a x)} x \sqrt {c-a c x} \, dx\) [447]
\(\int e^{-\text {arctanh}(a x)} \sqrt {c-a c x} \, dx\) [448]
\(\int \genfrac {}{}{}{}{e^{-\text {arctanh}(a x)} \sqrt {c-a c x}}{x} \, dx\) [449]
\(\int \genfrac {}{}{}{}{e^{-\text {arctanh}(a x)} \sqrt {c-a c x}}{x^2} \, dx\) [450]
\(\int \genfrac {}{}{}{}{e^{-\text {arctanh}(a x)} \sqrt {c-a c x}}{x^3} \, dx\) [451]
\(\int \genfrac {}{}{}{}{e^{-\text {arctanh}(a x)} \sqrt {c-a c x}}{x^4} \, dx\) [452]
\(\int e^{-2 \text {arctanh}(a x)} x^3 \sqrt {c-a c x} \, dx\) [453]
\(\int e^{-2 \text {arctanh}(a x)} x^2 \sqrt {c-a c x} \, dx\) [454]
\(\int e^{-2 \text {arctanh}(a x)} x \sqrt {c-a c x} \, dx\) [455]
\(\int e^{-2 \text {arctanh}(a x)} \sqrt {c-a c x} \, dx\) [456]
\(\int \genfrac {}{}{}{}{e^{-2 \text {arctanh}(a x)} \sqrt {c-a c x}}{x} \, dx\) [457]
\(\int \genfrac {}{}{}{}{e^{-2 \text {arctanh}(a x)} \sqrt {c-a c x}}{x^2} \, dx\) [458]
\(\int \genfrac {}{}{}{}{e^{-2 \text {arctanh}(a x)} \sqrt {c-a c x}}{x^3} \, dx\) [459]
\(\int \genfrac {}{}{}{}{e^{-2 \text {arctanh}(a x)} \sqrt {c-a c x}}{x^4} \, dx\) [460]
\(\int \genfrac {}{}{}{}{e^{-2 \text {arctanh}(a x)} \sqrt {c-a c x}}{x^5} \, dx\) [461]
\(\int e^{-3 \text {arctanh}(a x)} x^3 \sqrt {c-a c x} \, dx\) [462]
\(\int e^{-3 \text {arctanh}(a x)} x^2 \sqrt {c-a c x} \, dx\) [463]
\(\int e^{-3 \text {arctanh}(a x)} x \sqrt {c-a c x} \, dx\) [464]
\(\int e^{-3 \text {arctanh}(a x)} \sqrt {c-a c x} \, dx\) [465]
\(\int \genfrac {}{}{}{}{e^{-3 \text {arctanh}(a x)} \sqrt {c-a c x}}{x} \, dx\) [466]
\(\int \genfrac {}{}{}{}{e^{-3 \text {arctanh}(a x)} \sqrt {c-a c x}}{x^2} \, dx\) [467]
\(\int \genfrac {}{}{}{}{e^{-3 \text {arctanh}(a x)} \sqrt {c-a c x}}{x^3} \, dx\) [468]
\(\int \genfrac {}{}{}{}{e^{-3 \text {arctanh}(a x)} \sqrt {c-a c x}}{x^4} \, dx\) [469]
\(\int \genfrac {}{}{}{}{e^{-3 \text {arctanh}(a x)} \sqrt {c-a c x}}{x^5} \, dx\) [470]
\(\int e^{3 \text {arctanh}(a x)} (e x)^m \sqrt {c+a c x} \, dx\) [471]
\(\int e^{\text {arctanh}(a x)} (e x)^m \sqrt {c+a c x} \, dx\) [472]
\(\int e^{-\text {arctanh}(a x)} (e x)^m \sqrt {c+a c x} \, dx\) [473]
\(\int e^{-3 \text {arctanh}(a x)} (e x)^m \sqrt {c+a c x} \, dx\) [474]
\(\int e^{4 \text {arctanh}(a x)} (e x)^m \sqrt {c+a c x} \, dx\) [475]
\(\int e^{2 \text {arctanh}(a x)} (e x)^m \sqrt {c+a c x} \, dx\) [476]
\(\int e^{-2 \text {arctanh}(a x)} (e x)^m \sqrt {c+a c x} \, dx\) [477]
\(\int e^{-4 \text {arctanh}(a x)} (e x)^m \sqrt {c+a c x} \, dx\) [478]
\(\int e^{3 \text {arctanh}(a x)} (e x)^m \sqrt {c-a c x} \, dx\) [479]
\(\int e^{\text {arctanh}(a x)} (e x)^m \sqrt {c-a c x} \, dx\) [480]
\(\int e^{-\text {arctanh}(a x)} (e x)^m \sqrt {c-a c x} \, dx\) [481]
\(\int e^{-3 \text {arctanh}(a x)} (e x)^m \sqrt {c-a c x} \, dx\) [482]
\(\int e^{4 \text {arctanh}(a x)} (e x)^m \sqrt {c-a c x} \, dx\) [483]
\(\int e^{2 \text {arctanh}(a x)} (e x)^m \sqrt {c-a c x} \, dx\) [484]
\(\int e^{-2 \text {arctanh}(a x)} (e x)^m \sqrt {c-a c x} \, dx\) [485]
\(\int e^{-4 \text {arctanh}(a x)} (e x)^m \sqrt {c-a c x} \, dx\) [486]
\(\int e^{\text {arctanh}(a x)} (c-\genfrac {}{}{}{}{c}{a x})^4 \, dx\) [487]
\(\int e^{\text {arctanh}(a x)} (c-\genfrac {}{}{}{}{c}{a x})^3 \, dx\) [488]
\(\int e^{\text {arctanh}(a x)} (c-\genfrac {}{}{}{}{c}{a x})^2 \, dx\) [489]
\(\int e^{\text {arctanh}(a x)} (c-\genfrac {}{}{}{}{c}{a x}) \, dx\) [490]
\(\int \genfrac {}{}{}{}{e^{\text {arctanh}(a x)}}{c-\genfrac {}{}{}{}{c}{a x}} \, dx\) [491]
\(\int \genfrac {}{}{}{}{e^{\text {arctanh}(a x)}}{(c-\genfrac {}{}{}{}{c}{a x})^2} \, dx\) [492]
\(\int \genfrac {}{}{}{}{e^{\text {arctanh}(a x)}}{(c-\genfrac {}{}{}{}{c}{a x})^3} \, dx\) [493]
\(\int e^{2 \text {arctanh}(a x)} (c-\genfrac {}{}{}{}{c}{a x})^5 \, dx\) [494]
\(\int e^{2 \text {arctanh}(a x)} (c-\genfrac {}{}{}{}{c}{a x})^4 \, dx\) [495]
\(\int e^{2 \text {arctanh}(a x)} (c-\genfrac {}{}{}{}{c}{a x})^3 \, dx\) [496]
\(\int e^{2 \text {arctanh}(a x)} (c-\genfrac {}{}{}{}{c}{a x})^2 \, dx\) [497]
\(\int e^{2 \text {arctanh}(a x)} (c-\genfrac {}{}{}{}{c}{a x}) \, dx\) [498]
\(\int \genfrac {}{}{}{}{e^{2 \text {arctanh}(a x)}}{c-\genfrac {}{}{}{}{c}{a x}} \, dx\) [499]
\(\int \genfrac {}{}{}{}{e^{2 \text {arctanh}(a x)}}{(c-\genfrac {}{}{}{}{c}{a x})^2} \, dx\) [500]