Mathematics

# Find:$\displaystyle \int \dfrac {xe^{x}}{(1+x)^{2}}dx$

##### SOLUTION
$y = \int \frac{xe^{x}}{(1+x)^{2}}dx$
$y=\int [\frac{1}{1+x}-\frac{1}{(1+x)^{2}}]dx$
We know $\int e^{x}[f(x)-f(x)]=e^{x}f(x)$
then
$y=\int e^{x}[\frac{1}{1+x}-\frac{1}{(1+x)^{2}}]dx=\frac{e^{x}}{1+x}+c$

Its FREE, you're just one step away

Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 84

#### Realted Questions

Q1 Single Correct Medium
The value of $\displaystyle \int \dfrac{x^2+1}{x^4-x^2+1}dx$ is
• A. $\tan^{-1}(2x^2-1)+C$
• B. $\sin^{-1}\left(x-\dfrac{1}{x}\right)+C$
• C. $\tan^{-1}x^2+C$
• D. $\tan^{-1}\left(\dfrac{x^2-1}{x}\right)+C$

1 Verified Answer | Published on 17th 09, 2020

Q2 Subjective Hard
Evaluate the given integral.
$\displaystyle \int { x\left( \cfrac { \sec { 2x } -1 }{ \sec { 2x } +1 } \right) } dx$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Medium

$\displaystyle \int_{0}^{1}\frac{xdx}{(x^{2}+1)^{2}}=$
• A. $1/2$
• B. $1/3$
• C. $0$
• D. $1/4$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
Evaluate the integral:
$\displaystyle \int e^x\left(\frac{1+sinx}{1+cosx}\right) dx$

Consider two differentiable functions $f(x), g(x)$ satisfying $\displaystyle 6\int f(x)g(x)dx=x^{6}+3x^{4}+3x^{2}+c$ & $\displaystyle 2 \int \frac {g(x)dx}{f(x)}=x^{2}+c$. where $\displaystyle f(x)>0 \forall x \in R$