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Question Number 208205 by efronzo1 last updated on 07/Jun/24

∫ (x^3 . 5^(2x^2 −2) ) dx =?

∫(x3.52x2−2)dx=?

Answered by Frix last updated on 07/Jun/24

∫x^3 5^(2x^2 −2) dx=(1/(25))∫x^3 25^x^2 dx =^(t=x^2 ) (1/(50))∫25^t tdt =^(by parts) ((25^t t)/(100ln 5))−(1/(100ln 5))∫25^t dt= =((25^t t)/(100ln 5))−((25^t )/(200(ln 5)^2 ))= =((25^x^2 (2ln 5 x^2 −1))/(200(ln 5)^2 ))+C

∫x352x2−2dx=125∫x325x2dx=t=x2150∫25ttdt=byparts25tt100ln5−1100ln5∫25tdt==25tt100ln5−25t200(ln5)2==25x2(2ln5x2−1)200(ln5)2+C

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