### Home > CALC > Chapter 8 > Lesson 8.1.3 > Problem 8-32

8-32.

Let *U* = 2 − *e ^{x}*.

Don't forget to rewrite the bounds in terms of *u*.

The derivative of an INDEFINITE integral, is the original function (FTC, pt.1) But the derivative of a DEFINITE integral is the original function times the derivative of the bounds.

2*xf*(*x*^{2})

Let *u* = sec(*x*).

arctan(*u*) + *C* =

Now rewrite the answer in terms of *x*.

Recall that *x*^{4} = (*x*^{2})^{2}.

Use *u*-substitution.

And don't forget about the bounds!