### Home > CALC > Chapter 8 > Lesson 8.1.4 > Problem8-42

8-42.

No calculator! Evaluate the integrals below.

1. $\int _ { 2 } ^ { 4 } \frac { 1 } { 9 - 2 x } d x$

Before integrating, make a choice:
You could factor out $\frac{1}{2}$ or you could let U = 9 − 2x.

$\int \frac{1}{x}dx=\text{ln}\left | x \right |+C$
Don't forget the absolute value!

$\text{ln}|a|-\text{ln}|b|=\text{ln}\left | \frac{a}{b} \right |$

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

Notice the symmetrical bounds.Is this function odd? If so, the area will be 0. If not, integrate.

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

Factor before integrating.

1. $\int _ { 1 } ^ { 4 } \sqrt { 16 x ^ { 3 } } d x$

Recall that $\sqrt{16x^{3}}=4x^{\frac{3}{2}}$.

1. $\int _ { \pi / 4 } ^ { \pi / 2 } \operatorname { sin } ^ { 3 } x \operatorname { cos } x d x$

U-substitution. Should U = sinx or U = cosx?