# How do you find the integral of #f(x)=x^nsinx^(n-1)# using integration by parts?

##### 1 Answer

May 3, 2018

There's no closed form.

#### Explanation:

#I=intx^nsin(x^(n-1))dx#

Note that

#intx^(n-2)sin(x^(n-1))dx =1/(n-1)int(n-1)x^(n-2)sin(x^(n-1))dx#

#=1/(n-1)intsin(t)dt=cos(x^(n-1))/(n-1)#

Motivated by this integrable function, let's rewrite

#I=intx^2x^(n-2)sin(x^(n-1))dx#

Now, let

#I=uv-intvdu=(x^2cos(x^(n-1)))/(n-1)-2/(n-1)intxcos(x^(n-1))dx#

Unfortunately, this integral has no closed form. Did you type your question right?