Mathematics

# Evaluate: $\displaystyle \int \dfrac{2 x}{\left(x^{2}+4\right)} d x$

##### SOLUTION
$I=\displaystyle \int \dfrac {2x}{x^2+4} dx$

$t=x^2+4\implies dt=2xdx$

$=\displaystyle \int \dfrac 1tdt$

$=\displaystyle \log t$

$=\log (x^2+4)+c$

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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 Hard

lf $f(x)$ is a polynomial satisfying$f(x)f(\frac{1}{x})=f(x) +f(\frac{1}{x})$, and$f(3)=82$, then $\displaystyle \int\frac{f(x)}{x^{2}+1}dx=$
• A. $x^{3}-x+2\tan^{-1}x+c$
• B. $\displaystyle \frac{1}{3}x^{3}-x+\tan^{-1}x+c$
• C. $\displaystyle \frac{1}{3}x^{3}+x+2\tan^{-1}x+c$
• D. $\displaystyle \frac{x^{3}}{3}-x+2\tan^{-1}x +c$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Hard
$\displaystyle \lim_{n\rightarrow \infty }\frac{1^{p}+2^{p}+...+n^{p}}{n^{p+1}}$ is
• A. $\displaystyle \frac{1}{1-p}$
• B. $\displaystyle \frac{1}{p}-\frac{1}{p-1}$
• C. $\displaystyle \frac{1}{p+2}$
• D. $\displaystyle \frac{1}{p+1}$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Hard
If $f''(x)=-f(x)$ and $g(x)=f'(x)$ and $\displaystyle{F}({x})=\left ({f}\left (\frac{{x}}{2}\right)\right)^{2}+\left ({g}\left (\frac{{x}}{2}\right)\right)^{2}$ and given that $F(5)=5$, then $F(10)$ is equal to
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1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Medium
Compute the integral$\displaystyle \int_{0}^{1}\left ( e^{x}-1 \right )^{4}e^{x}dx$
• A. $\displaystyle \left ( e-1 \right )^{5}$
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Evaluate: $\displaystyle \overset{\pi/2}{\underset{0}{\int}} \sin x\cdot \sin 2x \,\,dx$.