`int t^3 e^(-t^2) dt` First make a substitution and then use integration by parts to evaluate the integral

Expert Answers

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Let `x=t^2`




Now apply integration by parts,

If f(x) and g(x) are differentiable functions then,


If we write f(x)=u and g'(x)=v, then


So, let's take u=x , then u'=1

and v=`e^-x`

then v'=`-e^-x`







substitute back `x=t^2` and add a constant to the solution,



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