Antiderivative of ;( (7x-2x^3)e^x^4-7x^2 )dx ?

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Antiderivative of ; $(7 x - 2 x^{3}) e^{x^{4} - 7 x^{2}} d x ?$ $(7x-2x^3)e^(x^4-7x^2 )dx ?$

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Answer 1 · 2018-04-28T19:39:54

$- \frac{1}{2} e^{x^{4} - 7 x^{2}} + C$ $-1/2e^(x^4-7x^2)+C$ .

Set, $x^4-7x^2=t. :. (4x^3-14x)dx=dt$ .

$:. 2(2x^3-7x)dx=dt, or, (2x^3-7x)dx=1/2dt$ .

$:. int(7x-2x^3)e^(x^4-7x^2)dx$ ,

$=-1/2inte^tdt$ ,

$=-1/2e^t$ ,

$=-1/2e^(x^4-7x^2)+C$ .