Use the substitution u = tan(x) to evaluate the following. int_0^(pi/6) (text(tan) ^2 x text( sec) ^4 x) text( ) dx

If we use the substitution , then . If you try substituting just and into the integrand, though, you'll notice that there's a left over that we have to deal with.

To get rid of this problem, use the identity and substitute in the left side of the identity for the extra , as shown:




From there, we can substitute in and , and then evaluate:

It’s going to be d. 4x^2-4x-19’