### Home > CALC > Chapter 7 > Lesson 7.4.4 > Problem7-210

7-210.

Multiple Choice: $\int \operatorname { cos } \sqrt { x } d x =$

1. $\operatorname{sin}\sqrt { x }+C$

1. $2x \operatorname{sin} x − 2 \operatorname{sin} x + C$

1. $2\sqrt { x }\operatorname{sin}\sqrt { x }+ 2 \operatorname{cos}\sqrt { x }+ C$

1. $2x \operatorname{cos} x − 2 \operatorname{sin} x + C$

1. $2\sqrt { x }\operatorname{cos}\sqrt { x }+ 2 \operatorname{cos}\sqrt { x }+ C$

First use $u$-Sub:

Then use integration by parts:

$U=\sqrt{x}$

$\frac{dU}{dx}=\frac{1}{2\sqrt{x}}$

$2\sqrt{x}dU=dx=2UdU$

$\int 2U\text{cos}(U)dU$

Let $f(x) = 2U$ and $dg =\operatorname{cos}(U)dU$
Find $df =$ __________ and $g\left(x\right) =$ ____________.

$\text{Then evaluate: }f(x)g(x)-\int g(x)df$