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

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

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Answer 1 · 2018-04-28T19:39:54

# -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#.