Mathematics

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


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

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

$$=\displaystyle \int  \dfrac 1tdt$$

$$=\displaystyle \log t$$

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

Its FREE, you're just one step away


Subjective Medium Published on 17th 09, 2020
Next Question
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 84
Enroll Now For FREE

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. $$\displaystyle \frac{x^{3}}{3}-x+2\tan^{-1}x +c$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
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. $$\displaystyle \frac{1}{p+1}$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
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 
  • A. $$10$$
  • B. $$0$$
  • C. $$15$$
  • D. $$5$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q4 Single Correct Medium
Compute the integral$$\displaystyle \int_{0}^{1}\left ( e^{x}-1 \right )^{4}e^{x}dx$$
  • A. $$\displaystyle \left ( e-1 \right )^{5}$$
  • B. $$\displaystyle 0.5\left ( e-1 \right )^{5}$$
  • C. None of the above
  • D. $$\displaystyle 0.2\left ( e-1 \right )^{5}$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q5 Subjective Medium
Evaluate: $$\displaystyle \overset{\pi/2}{\underset{0}{\int}} \sin x\cdot \sin 2x \,\,dx$$.

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer