### Home > APCALC > Chapter 10 > Lesson 10.1.6 > Problem10-70

10-70.

Examine the integrals below. Consider the multiple tools available for integrating and use the best strategy for each part. Evaluate each integral and briefly describe your method. Homework Help ✎

1. $\int \frac { 1 } { ( x - 1 ) ( x + 5 ) } d x$

Use partial fraction decomposition.

1. $\int \frac { x ^ { 3 } + 2 x } { x - 1 } d x$

Rewrite the integrand by using polynomial division.

1. $\int 5 x ^ { 2 } ( 5 x ^ { 3 } - 2 ) ^ { - 1 / 2 } d x$

Use substitution. Let $u = 5x^3 - 2$.

1. $- \int 2 \operatorname { sec } ^ { 2 } ( x ) d x$

$\frac{d}{dx}\tan(x)=\sec^2(x)$