Mathematics

# $\displaystyle \int \dfrac{dx}{e^x + e^{-x} +2}$ is equal to

$\dfrac{-1}{e^x+1} +C$

##### SOLUTION
$\displaystyle \int \dfrac{dx}{e^x + e^{-x} +2}$

$\displaystyle =\int \dfrac{e^x}{e^{2x}+2e^x+1}dx$
Put $e^x=t$

$\Rightarrow e^xdx=dt$

$\displaystyle \therefore I=\int \dfrac{dt}{t^2+2t+1}$

$\displaystyle =\int \dfrac{dt}{(t+1)^2}$

$=\dfrac{-1}{t+1}+C$

$=\dfrac{-1}{e^x+1}+C$

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Single Correct Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 109

#### Realted Questions

Q1 Single Correct Hard
Match the elements of List I with List II:
 List-I List-II A) $\displaystyle \int_{0}^{\frac{\pi}{2}}\log\sin{x}\>dx=$ 1) $4\pi$ B) $\displaystyle \int_{0}^{\frac{\pi}{2}}\log\tan x\>dx=$ 2) $-\dfrac{\pi}{2}\log_e2$ C) $\displaystyle\int_{0}^{\pi}x\log\sin x\>dx=$ 3) $-\dfrac{{\pi}^2}{2}\log_e2$ D) $\displaystyle\int_{-\pi}^{\pi}(x^{3}+x\cos x+\tan^{5}x+2)dx =$ 4) $0$
• A. $A-3, B-4, C-1, D-2$
• B. $A-1, B-4, C-2, D-3$
• C. $A-3, B-2, C-2, D-1$
• D. $A-2, B-4, C-3, D-1$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Hard
The integral $\int \dfrac {2x^{12} + 5x^{9}}{(x^{5} + x^{3} + 1)^{3}} dx$ is equal to:
• A. $\dfrac {-x^{5}}{(x^{5} + x^{3} + 1)^{2}} + C$
• B. $\dfrac {x^{5}}{2(x^{5} + x^{3} + 1)^{2}} + C$
• C. $\dfrac {-x^{-10}}{2(x^{5} + x^{3} + 1)^{2}} + C$
• D. $\dfrac {x^{10}}{2(x^{5} + x^{3} + 1)^{2}} + C$

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Medium
$\int \dfrac{{{x^5}}}{{\sqrt {1 - {x^{12}}} }}\;dx$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
Express the following integral as limits of sum and hence evalute it. $\int_{0}^{4}\left ( x-x^{2} \right )dx$

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 $\displaystyle f(x)>0 \forall x \in R$