Mathematics

# Solve: $\displaystyle \int \dfrac{x^3}{x - 2}dx$

##### SOLUTION
$\displaystyle\int \dfrac{x^3}{x-2}dx$
$=\displaystyle\int \left[\dfrac{(x-2)(x^2+2x+4)+8}{(x-2)}\right]dx$
$=\displaystyle\int \left[(x^2+2x+4)+\dfrac{8}{x-2}\right]dx$
$=\dfrac{x^3}{3}+x^2+4x+8 ln(x-2)+c$
$\therefore \displaystyle\int \dfrac{x^3}{x-2}dx=\dfrac{x^3}{3}+x^2+4x+8 ln(x-2)+c$

$x^2+2x+4$
$x-2) x^3$
$x^3-2x^3$
________________
$2x^2$
$2x^2-4x$
_____________
$4x$
$4x-8$
__________
$8$.

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Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 111

#### Realted Questions

Q1 Single Correct Medium
$\dfrac {(1)}{(2-3x)^4} dx=$ ?
• A. $\dfrac {(1)}{(2-3x)^4}+C$
• B. $\dfrac {(1)}{-12(2-3x)^3}+C$
• C. none of these
• D. $\dfrac {(1)}{9(2-3x)^3}+C$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Hard
The value of $\int \dfrac {10^{x/2}}{\sqrt {10^{-x} - 10^{x}}}\, dx$ is
• A. $2\sqrt {10^{-x} + 10^{x}} + c$
• B. $\dfrac {1}{\log_{e}10}\sin h^{-1} (10^{x}) + c$
• C. $\dfrac {-1}{\log_{e}10}\sin h^{-1}(10^{x}) + c$
• D. $\dfrac {1}{\log_{2}10}\sin^{-1}(10^{x}) + c$

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Medium
Evaluate: $\displaystyle \int _0^2 \dfrac x 3 dx$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
Evaluate $\displaystyle\int^{\pi/2}_0\sqrt{1+\cos x}dx$.

$\int \frac{2x^{2}}{3x^{4}2x} dx$