### Home > APCALC > Chapter 7 > Lesson 7.3.1 > Problem7-102

7-102.

No calculator! Integrate.

1. $\int ( 3 e ^ { 4 x } + 2 ^ { x } ) d x$

$e$ is NOT a variable.

1. $\int _ { 0 } ^ { \pi } \operatorname { sin } ^ { 3 } ( x ) \operatorname { cos } ( x ) d x$

Let $u=\sin\left(x\right)$.

1. $\int x ^ { 2 } ( 3 x ^ { 3 } + 5 ) ^ { 4 } d x$

Notice that the term in parentheses has a highest-power of $3$, while the term outside of the parenthesis has a power of $2$.
$U$-substitution!

1. $\int \frac { 5 x ^ { 0.25 } } { 4 x ^ { 1.25 } - 6 } d x$

Refer to the hint in part (c).

1. $\int _ { e } ^ { e ^ { 3 } } \frac { 1 } { x } \operatorname { ln } ( x ) d x$

What is the derivative of $\ln\left(x\right)$?

1. $\int _ { 0 } ^ { 1 } \frac { 1 } { \sqrt { 1 - x ^ { 2 } } } d x$

Inverse trig.