Mathematics

Solve $$\displaystyle\int\dfrac{e^x(x-1)}{(x+1)^3}dx$$


ANSWER

$$\dfrac{{{e^x}}}{{{{\left( {x + 1} \right)}^2}}} + c$$


SOLUTION
$$=\displaystyle\int \dfrac{e^{x}(x-1)}{x+1}^{3}dx$$
$$=\displaystyle\int \dfrac{e^{x}(x+1)}{(x+1)^{3}}dx-2\int \dfrac{e^{x}}{(x+1)}dx$$
$$=\displaystyle\int \dfrac{e^{x}dx}{(x+1)^{2}}-2\int \dfrac{e^{x}}{(x+1)^{3}}dx$$
Applying integration by  parts on  firsttem 
$$\dfrac{e^{x}}{(x+1)^{2}}+^{2}\displaystyle\int \dfrac{e^{x}}{(x+1)^{3}}-\int \dfrac{e^{x}}{(x+1)^{3}}+c$$
$$\dfrac{e^{x}}{(x+1)^{2}}+c.$$
$$B$$ is correct
View Full Answer

Its FREE, you're just one step away


Single Correct Medium Published on 17th 09, 2020
Next Question
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 84
Enroll Now For FREE

Realted Questions

Q1 Single Correct Hard
Let $$f$$ be a positive function. Let $$\displaystyle I_1=\int_{\displaystyle 1-k}^{\displaystyle k}{(x)f(x(1-x))dx}$$; $$\displaystyle I_2=\int_{\displaystyle 1-k}^{\displaystyle k}{f(x(1-x))dx}$$, where $$2k-1>0$$. Then, $$\displaystyle\frac{I_2}{I_1}$$ is
  • A. $$k$$
  • B. $$\displaystyle\frac{1}{2}$$
  • C. $$1$$
  • D. $$2$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q2 Single Correct Hard
The value of $$\displaystyle\int _{ 0 }^{ \tfrac { \pi  }{ 2 }  }{ \frac { \cos ^{ \frac { 5 }{ 3 }  }{ x }  }{ \cos ^{ \frac { 5 }{ 3 }  }{ x } +\sin ^{ \frac { 5 }{ 3 }  }{ x }  } dx } $$ is
  • A. $$\dfrac { \pi }{ 2 } $$
  • B. $$0$$
  • C. $$\pi$$
  • D. $$\dfrac { \pi }{ 4 } $$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q3 Single Correct Medium
Evaluate:$$\displaystyle\int \frac{cos\,x}{\sqrt{9sin^{2}x-1}}dx $$
  • A. $$ \log\left | 3 \sin\,x+\sqrt{9 \sin^{2}x-1} \right |+C $$
  • B. $${3} \log\left | 3 \sin\,x+\sqrt{9 \sin^{2}x-1} \right |+C $$
  • C. none of these
  • D. $$\dfrac{1}{3} \log\left | 3 \sin\,x+\sqrt{9 \sin^{2}x-1} \right |+C $$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q4 Subjective Hard
Evaluate : $$\displaystyle \int_0^{\pi} \dfrac{x  \sin  x}{1 + \sin  x} dx$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q5 Subjective Easy
Evaluate $$\int \dfrac{e^x-e^{-x}}{e^x+e^{-x}}dx$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer