Mathematics

# Integrate $\displaystyle\int \dfrac{(5x^2+7x+3)}{(x+1)}dx$

##### SOLUTION
$\int { \dfrac { { 5x }^{ 2 }+7x+3 }{ x+1 } } dx$
$\int { \dfrac { { 5x }^{ 2 }+5x+2x+2+1 }{ x+1 } } dx$
$=\int { \dfrac { { 5x }^{ 2 }+5x }{ x+1 } dx } +\int { \dfrac { 2x+2 }{ x+1 } dx } +\int { \dfrac { 1 }{ x+1 } dx }$
$=\int { 5xdx } +\int { 2dx } +\int { \dfrac { 1 }{ x+1 } dx }$
$=\dfrac { { 5x }^{ 2 } }{ 2 } +2x+ln\left| x+1 \right| +C$

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

#### Realted Questions

Q1 Single Correct Hard
$\displaystyle\int { \cfrac { \left( 2{ x }^{ 12 }+5{ x }^{ 9 } \right) }{ { \left( 1+{ x }^{ 3 }+{ x }^{ 5 } \right) }^{ 3 } } } dx$ equals
• A. $\cfrac { { x }^{ 2 }+2x }{ \left( { x }^{ 5 }+{ x }^{ 3 }+1 \right) } +C$
• B. $\log { \left[ { x }^{ 5 }+{ x }^{ 3 }+1+\sqrt { 2{ x }^{ 12 }+5{ x }^{ 9 } } +C \right] }$
• C. None of the above
• D. $\cfrac { { x }^{ 10 } }{ 2{ \left( { x }^{ 5 }+{ x }^{ 3 }+1 \right) }^{ 2 } } +C$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium

$\displaystyle \int_{0}^{1/2}\frac{x\sin^{-1}x}{\sqrt{1-x^{2}}}dx_{=}$
• A. $\displaystyle \frac{1}{2}+\frac{\pi\sqrt{3}}{12}$
• B. $\displaystyle \frac{\pi\sqrt{3}}{12}$
• C. $\displaystyle \frac{-\pi\sqrt{3}}{12}$
• D. $\displaystyle \frac{1}{2}-\frac{\pi\sqrt{3}}{12}$

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Medium
Solve: $\displaystyle \int \dfrac{\log^x}{x^3}dx$

1 Verified Answer | Published on 17th 09, 2020

Q4 One Word Medium
Let $I = \int_1^3 | (x - 1) (x - 2) (x - 3) |dx$. The value of $I^{-1}$ is

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