3.5 Integrals 401 to 500

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