Mathematics

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

##### SOLUTION
Put $x+1=t\\dx=dt\\\displaystyle \int \dfrac1{t^2}dt\\\displaystyle \int t^{-2} dt\\\dfrac {t^{-1}}{-1}=-\dfrac 1t +c=\dfrac{-1}{1+x}+c$

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

#### Realted Questions

Q1 Single Correct Medium
Match the following.
I.$\displaystyle \int e^{x}(\sin x+\cos x)dx=$               a)$e^{x}\tan x+c$
II.$\ \displaystyle \int e^{x}(\cos x-\sin x)dx=$            b)$e^{x}\log\sec x+c$
III.$\ \displaystyle \int e^{x}(\tan x+\sec^{2}x)dx=$        c)$e^{x}\sin x+c$
IV. $\displaystyle \int e^{x} (\tan x+ \log \sec x)dx=$     d)$e^{x}\cos x+c$
• A. I-a, II- b, III- c, IV- d
• B. I-b, II- c, III- a, IV- d
• C. I-b, II- d, III- c, IV- a
• D. I-c, II- d, III- a, IV- b

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
The value of $\int_{0}^{[x]} (x-[x])dx$, where $[x]$ is the greatest integer $|le x$ is equal to
• A. $2[x]$
• B. $\dfrac{1}{2} [x]$
• C. $\dfrac{1}{5} [x]$
• D. $4[x]$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Hard
$\int_{-1}^{1}(3-5x-6x^{2})e^{-x^{2}}dx=$

• A. $\dfrac{1}{e}$
• B. $\dfrac{2}{e}$
• C. $\dfrac{3}{e}$
• D. $\dfrac{6}{e}$

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Hard
If $\displaystyle \int\log(\sqrt{1-x}+\sqrt{1+x})dx=xf(x)+Ax +B\sin^{-1}x+c$, then
• A. $\displaystyle A=-\frac{1}{3}$
• B. $\displaystyle B= \frac{2}{3}$
• C. $\displaystyle B=- \frac{1}{2}$
• D. $\displaystyle f(x)=\log(\sqrt{1-x}+\sqrt{1+x})$

Let $\displaystyle f\left ( x \right )=\frac{\sin 2x \cdot \sin \left ( \dfrac{\pi }{2}\cos x \right )}{2x-\pi }$