Mathematics

# $\int e^{x}[\frac{x^{2}+1}{(x+1)^{2}}]dx$=

$e^{x}(\frac{x-1}{x+1})+c$

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Single Correct Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 86

#### Realted Questions

Q1 Single Correct Medium
The value of $\displaystyle \int_{-1}^{1}x|x|dx$ is
• A. $2$
• B. $1$
• C. None of these
• D. $0$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
The integral $\displaystyle\int\dfrac{\sin^2x\cos^2x}{(\sin^5x+\cos^3x\sin^2x+\sin^3x\cos^2x+\cos^5x)^2}dx$ is equal to?
• A. $\dfrac{1}{1+\cot^3x}+C$
• B. $\dfrac{-1}{1+\cot^3x}+C$
• C. $\dfrac{1}{3(1+\tan^3x)}+C$
• D. $\dfrac{-1}{3(1+\tan^3x)}+C$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Hard
I = $\int\dfrac{dx}{\sqrt{x}(x+9)}$ is equal to
• A. $\dfrac{2}{3}\tan^{-1}(\sqrt{x})+c$
• B. $\tan^{-1}(\dfrac{\sqrt{x}}{3})+c$
• C. $\dfrac{2}{5}\tan^{-1}(\dfrac{\sqrt{x}}{5})+c$
• D. $\dfrac{2}{3}\tan^{-1}(\dfrac{\sqrt{x}}{3})+c$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
Evaluate the following definite integral:
$\displaystyle \int _{\pi /4}^{\pi /2} \cot x \ dx$

Let $\displaystyle 2I_{1}+I_{2}=\int \frac {e^{x}}{e^{2x}+e^{-2x}}dx$  and  $\displaystyle I_{1}+2I_{2}=\int \frac {e^{-x}}{e^{2x}+e^{-2x}}dx$