Mathematics

# Integrate: $\dfrac { 3 x - 1 } { ( x + 2 ) ^ { 2 } }$

##### SOLUTION
$I =\displaystyle \int \dfrac{3x-1}{(x+2)^{2}}dx$

$u = x+2 \Rightarrow x = u-2 \Rightarrow dx = du$

$I = \displaystyle\int \dfrac{3(u-2)-1}{u^{2}}du$

$I =\displaystyle \int \dfrac{3u-7}{u^{2}}du = \int \left(\dfrac{3}{u}-\dfrac{7}{u^{2}}\right)du$

$I = 3 \ln u+\dfrac{7}{u}+c$

$I = 3 \ln \left | x+2 \right |+\dfrac{7}{x+2}+c$

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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
Solve $\displaystyle\int \frac{\sec ^{4}x}{\sqrt{\left ( \tan x \right )}}dx$
• A. $\displaystyle \frac{2}{5}\sqrt{\tan x}\left ( 5-\tan ^{2}x\right ).$
• B. $\displaystyle \frac{2}{7}\sqrt{\tan x}\left ( 5+\tan ^{2}x\right ).$
• C. $\displaystyle \frac{2}{7}\sqrt{\tan x}\left ( 5+\tan ^{3}x\right ).$
• D. $\displaystyle \frac{2}{5}\sqrt{\tan x}\left ( 5+\tan ^{2}x\right ).$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
The value of the integral $\displaystyle\int^{1}_{\dfrac{1}{3}}\dfrac{(x-x^3)^{\dfrac{1}{3}}}{x^4}dx$ is?
• A. $0$
• B. $3$
• C. $4$
• D. $6$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Medium
Evaluate: $\displaystyle\int x e^{x^2log 2}\cdot e^{x^2}dx=$
• A. $\displaystyle\frac{2^{x^2}\cdot e^{x^2}}{1+log 2}$
• B. $\displaystyle\frac{e^{x^2log 2}\cdot e^{x^2}}{log 2}$
• C. $\displaystyle\frac{(2e)^{x^2}}{log (2e)}$
• D. $\displaystyle\frac{2^{x^2}\cdot e^{x^2}}{2(1+log 2)}$

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Hard

$\displaystyle \int_{0}^{\pi}\frac{\sin(2n-1)x}{\sin x}dx,\ (n\in N)$ is equal to
• A. 1
• B. $\displaystyle \frac{\pi}{2}$
• C. $2\pi$
• D. $\pi$

$\displaystyle\int \dfrac{1}{e^x+e^{-x}}dx$.