Question

Why cant I use substitute method on integrating x^2sinx

Answer 1

Because there is nothing to call u there. I mean, if u = x^2, then du = 2xdx and if u = sinx, du = cosxdx

Answer 2

Neither show up in the integral :-)

Answer 3

Because neither gives you the derivative of the other function. So you have to use parts

Answer 4

yep what the heck are you going to use as your u?

Answer 5

To use sub, if u = x^2, then du has to be 2x, but sinx is no where near that.

Answer 6

The general idea behind the substitution method is that you recognize an inverted chain rule operation. Such that\[\int g(x)\,dx=\int f'(x)f(x)\,dx\]The only exception I can think of the top of my head is some operation like\[\int\frac{1}{\ln x}\,dx,\,u=\ln x,\,du=\frac{1}{x}dx,\,dx=x\,du,\,dx=e^{\ln x}\,du,\,dx=d^u\,du\]