3.5 Integrals 401 to 454

\(\int (a d+b d x)^m (a^2 c+2 a b c x+b^2 c x^2) \, dx\) [401]
\(\int (a d+b d x)^m \, dx\) [402]
\(\int \genfrac {}{}{}{}{(a d+b d x)^m}{a^2 c+2 a b c x+b^2 c x^2} \, dx\) [403]
\(\int \genfrac {}{}{}{}{(a d+b d x)^m}{(a^2 c+2 a b c x+b^2 c x^2)^2} \, dx\) [404]
\(\int \genfrac {}{}{}{}{(a d+b d x)^m}{(a^2 c+2 a b c x+b^2 c x^2)^3} \, dx\) [405]
\(\int (a d+b d x)^m (a^2 c+2 a b c x+b^2 c x^2)^{3/2} \, dx\) [406]
\(\int (a d+b d x)^m \sqrt {a^2 c+2 a b c x+b^2 c x^2} \, dx\) [407]
\(\int \genfrac {}{}{}{}{(a d+b d x)^m}{\sqrt {a^2 c+2 a b c x+b^2 c x^2}} \, dx\) [408]
\(\int \genfrac {}{}{}{}{(a d+b d x)^m}{(a^2 c+2 a b c x+b^2 c x^2)^{3/2}} \, dx\) [409]
\(\int \genfrac {}{}{}{}{(a d+b d x)^m}{(a^2 c+2 a b c x+b^2 c x^2)^{5/2}} \, dx\) [410]
\(\int (d+e x)^m (a^2+2 a b x+b^2 x^2)^3 \, dx\) [411]
\(\int (d+e x)^m (a^2+2 a b x+b^2 x^2)^2 \, dx\) [412]
\(\int (d+e x)^m (a^2+2 a b x+b^2 x^2) \, dx\) [413]
\(\int \genfrac {}{}{}{}{(d+e x)^m}{a^2+2 a b x+b^2 x^2} \, dx\) [414]
\(\int \genfrac {}{}{}{}{(d+e x)^m}{(a^2+2 a b x+b^2 x^2)^2} \, dx\) [415]
\(\int \genfrac {}{}{}{}{(d+e x)^m}{(a^2+2 a b x+b^2 x^2)^3} \, dx\) [416]
\(\int (d+e x)^m (a^2+2 a b x+b^2 x^2)^{5/2} \, dx\) [417]
\(\int (d+e x)^m (a^2+2 a b x+b^2 x^2)^{3/2} \, dx\) [418]
\(\int (d+e x)^m \sqrt {a^2+2 a b x+b^2 x^2} \, dx\) [419]
\(\int \genfrac {}{}{}{}{(d+e x)^m}{\sqrt {a^2+2 a b x+b^2 x^2}} \, dx\) [420]
\(\int \genfrac {}{}{}{}{(d+e x)^m}{(a^2+2 a b x+b^2 x^2)^{3/2}} \, dx\) [421]
\(\int \genfrac {}{}{}{}{(d+e x)^m}{(a^2+2 a b x+b^2 x^2)^{5/2}} \, dx\) [422]
\(\int (d+e x)^3 (c d^2+2 c d e x+c e^2 x^2)^p \, dx\) [423]
\(\int (d+e x) (c d^2+2 c d e x+c e^2 x^2)^p \, dx\) [424]
\(\int \genfrac {}{}{}{}{(c d^2+2 c d e x+c e^2 x^2)^p}{d+e x} \, dx\) [425]
\(\int \genfrac {}{}{}{}{(c d^2+2 c d e x+c e^2 x^2)^p}{(d+e x)^3} \, dx\) [426]
\(\int \genfrac {}{}{}{}{(c d^2+2 c d e x+c e^2 x^2)^p}{(d+e x)^5} \, dx\) [427]
\(\int (d+e x)^4 (c d^2+2 c d e x+c e^2 x^2)^p \, dx\) [428]
\(\int (d+e x)^2 (c d^2+2 c d e x+c e^2 x^2)^p \, dx\) [429]
\(\int (c d^2+2 c d e x+c e^2 x^2)^p \, dx\) [430]
\(\int \genfrac {}{}{}{}{(c d^2+2 c d e x+c e^2 x^2)^p}{(d+e x)^2} \, dx\) [431]
\(\int \genfrac {}{}{}{}{(c d^2+2 c d e x+c e^2 x^2)^p}{(d+e x)^4} \, dx\) [432]
\(\int (d+e x)^3 (a^2+2 a b x+b^2 x^2)^p \, dx\) [433]
\(\int (d+e x)^2 (a^2+2 a b x+b^2 x^2)^p \, dx\) [434]
\(\int (d+e x) (a^2+2 a b x+b^2 x^2)^p \, dx\) [435]
\(\int (a^2+2 a b x+b^2 x^2)^p \, dx\) [436]
\(\int \genfrac {}{}{}{}{(a^2+2 a b x+b^2 x^2)^p}{d+e x} \, dx\) [437]
\(\int \genfrac {}{}{}{}{(a^2+2 a b x+b^2 x^2)^p}{(d+e x)^2} \, dx\) [438]
\(\int \genfrac {}{}{}{}{(a^2+2 a b x+b^2 x^2)^p}{(d+e x)^3} \, dx\) [439]
\(\int (d+e x)^{3/2} (a^2+2 a b x+b^2 x^2)^p \, dx\) [440]
\(\int \sqrt {d+e x} (a^2+2 a b x+b^2 x^2)^p \, dx\) [441]
\(\int \genfrac {}{}{}{}{(a^2+2 a b x+b^2 x^2)^p}{\sqrt {d+e x}} \, dx\) [442]
\(\int \genfrac {}{}{}{}{(a^2+2 a b x+b^2 x^2)^p}{(d+e x)^{3/2}} \, dx\) [443]
\(\int \genfrac {}{}{}{}{(a^2+2 a b x+b^2 x^2)^p}{(d+e x)^{5/2}} \, dx\) [444]
\(\int (d+e x)^m (c d^2+2 c d e x+c e^2 x^2)^p \, dx\) [445]
\(\int (d+e x)^p (c d^2+2 c d e x+c e^2 x^2)^{-p} \, dx\) [446]
\(\int (d+e x)^{-1-2 p} (c d^2+2 c d e x+c e^2 x^2)^p \, dx\) [447]
\(\int (d+e x)^{-1+2 p} (c d^2+2 c d e x+c e^2 x^2)^{-p} \, dx\) [448]
\(\int (1+x)^m (1+2 x+x^2)^p \, dx\) [449]
\(\int (\genfrac {}{}{}{}{b e}{2 c}+e x)^m (\genfrac {}{}{}{}{b^2}{4 c}+b x+c x^2)^p \, dx\) [450]
\(\int (d+e x)^m (a^2+2 a b x+b^2 x^2)^p \, dx\) [451]
\(\int (d+e x)^m (a^2+2 a b x+b^2 x^2)^{5+p} \, dx\) [452]
\(\int (d+e x)^{-3-2 p} (a^2+2 a b x+b^2 x^2)^p \, dx\) [453]
\(\int (d+e x) (9+12 x+4 x^2)^p \, dx\) [454]