$\text { Find the integral } \int \frac { 15 } { 2 \sqrt { x } ( 1 + x ) } d x \text {. }$
A) $\frac { 30 } { \arctan ( \sqrt { x } ) } + C$
B) $15 \arctan ( \sqrt { x } ) + C$
C) $\frac { 15 } { 2 \arctan ( \sqrt { x } ) } + C$
D) $\quad 30 \arctan ( \sqrt { x } ) + C$
E) $\frac { 15 } { \arctan ( \sqrt { x } ) } + C$

Question

$\text { Find the integral } \int \frac { 15 } { 2 \sqrt { x } ( 1 + x ) } d x \text {. }$ 
A) $\frac { 30 } { \arctan ( \sqrt { x } ) } + C$
B) $15 \arctan ( \sqrt { x } ) + C$
C) $\frac { 15 } { 2 \arctan ( \sqrt { x } ) } + C$
D) $\quad 30 \arctan ( \sqrt { x } ) + C$
E) $\frac { 15 } { \arctan ( \sqrt { x } ) } + C$

Quizplus · Accepted Answer

The integral can be solved by substituting $u = \sqrt{x}$, which leads to $du = \frac{1}{2\sqrt{x}}dx$. This transforms the integral into a form that integrates to $15 \arctan(u) + C$, and substituting back $u = \sqrt{x}$ gives $15 \arctan(\sqrt{x}) + C$.

Find the integral ∫152x(1+x)dx. \text { Find the integral } \int \frac { 15 } { 2 \sqrt { x } ( 1 + x ) } d x \text {. } Find the integral ∫2x​(1+x)15​dx.

$\text { Find the integral } \int \frac { 15 } { 2 \sqrt { x } ( 1 + x ) } d x \text {. }$