Mathematics

# $\displaystyle\int \left(e^x\right)^2 e^x dx$ is equal to

##### SOLUTION
Now,
$\displaystyle\int \left(e^x\right)^2 e^x dx$
$=\displaystyle\int \left(e^x\right)^2 d(e^x)$
$=\dfrac{(e^x)^3}{3}+c$ [ Where $c$ being integrating constant]
$=\dfrac{e^{3x}}{3}+c$

Its FREE, you're just one step away

Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 111

#### Realted Questions

Q1 Subjective Medium
$\dfrac { d y } { d x } = ( 4 x + y + 1 ) ^ { 2 }$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Hard
The value of $\displaystyle \int \frac{(ax^{2}-b)dx}{x\sqrt{c^{2}x^{2}-(ax^{2}+b)^{2}}}$ is equal to
• A. $\displaystyle \frac{1}{c}\sin^{-1}\left ( ax+\frac{b}{x} \right )+k$
• B. $\displaystyle c\sin^{-1}\left ( a+\frac{b}{x} \right )+k$
• C. none of these
• D. $\displaystyle \sin^{-1}\left ( \frac{ax+\frac{b}{x}}{c} \right )+k$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Hard
$\displaystyle\int{\frac{1}{(x+1)\sqrt{2+x-x^2}}dx}$ is equal to
• A. $\displaystyle \frac{2}{3}\sqrt{3\left(\frac{1}{x-1}\right)-1}+C$
• B. $\displaystyle \frac{3}{2}\sqrt{3\left(\frac{1}{x-1}\right)-1}+C$
• C. $\displaystyle-\frac{4}{3}\sqrt{3\left(\frac{1}{x-1}\right)-1}+C$
• D. $\displaystyle-\frac{2}{3}\sqrt{3\left(\frac{1}{x+1}\right)-1}+C$

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Medium
$\int {[f(x)g\prime \prime (x) - f\prime \prime (x)g(x)]} dx$ is equal to
• A. $\dfrac{{f\prime (x)}}{{g\prime (x)}}$
• B. $f\prime (x)g(x) - f(x)g\prime (x)$
• C. $f(x)g\prime (x) + f\prime (x)g(x)$
• D. $f(x)g\prime (x) - f\prime (x)g(x)$

Evaluate $\int \dfrac{e^x-e^{-x}}{e^x+e^{-x}}dx$