Mathematics

# Solve$\Rightarrow \int dx=\int \left(2+\dfrac{1}{v+2}\right)dv$

##### SOLUTION
$\displaystyle \int 1dx = \int \left(2 + \dfrac{1}{v + 2} \right)dv$
$\displaystyle \int 1 dx = \int 2 dv + \int \dfrac{1}{v + 2} dv$
$x = 2v + \log (v + 2) + c$

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

#### Realted Questions

Q1 Subjective Medium
Solve$\displaystyle \int_0^1 \dfrac{x^2-2}{x^2+1}dx$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
If $\displaystyle I = \int \frac {dx}{(e^x + 2)^3}$, then I equals
• A. $\displaystyle \frac {1}{8} x + \frac {1}{8} \log (e^x + 2) + \frac {e^x}{4(e^x + 2)^2} + C$
• B. $\displaystyle \frac {1}{8} x + \frac {1}{8} \log (e^x + 2) + \frac {e^x}{(e^x + 2)^2} + C$
• C. none of these
• D. $\displaystyle \frac {1}{8} x - \frac {1}{8} \log (e^x + 2) + \frac {e^x + 3}{4 (e^x + 2)^2} + C$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Hard
If $\int \sqrt{2 + \tan^2 x} dx = \ln (\tan x + \sqrt{2 + \tan^2 x}) + f(x) + c$, where $f(x)=$
• A. $\cos^{-1} \left(\dfrac{\sin x}{\sqrt 2} \right)$
• B. $\cos^{-1} \left(\dfrac{\cos x}{\sqrt 2} \right)$
• C. $\sin^{-1} \left(\dfrac{\cos x}{\sqrt 2} \right)$
• D. $\sin^{-1} \left(\dfrac{\sin x}{\sqrt 2} \right)$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
Integrate the rational function   $\cfrac {1}{x^4-1}$

1 Verified Answer | Published on 17th 09, 2020

Q5 Single Correct Medium
$\displaystyle \frac{3x-1}{(1-x+x^{2})(2+x)}=$
• A. $\displaystyle \frac{x}{x^{2}-x+1}+\frac{1}{x+2}$
• B. $\displaystyle \frac{x}{x^{2}+x+1}+\frac{2}{x+2}$
• C. $\displaystyle \frac{x}{ -x+1}-\frac{2}{x+2}$
• D. $\displaystyle \frac{x}{x^{2}-x+1}-\frac{1}{x+2}$