Mathematics

# Evaluate:$\int { \cfrac { { x }^{ 2 } }{ \left( 1+{ x }^{ 3 } \right) } } dx$

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

#### Realted Questions

Q1 Single Correct Medium
If $l_{n}=\displaystyle \int{\dfrac{t^{n}}{1+t^{2}}}dt$ then
• A. $l_{n+1}=\dfrac{t^{n+1}}{n+1}l_{n}$
• B. $l_{n+1}=\dfrac{t^{n-1}}{n-1}l_{n}$
• C. $l_{n21}=\dfrac{t^{n+1}}{n+1}l_{n}$
• D. $l_{n+2}=\dfrac{t^{n}}{n}-nl_{n}$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Hard
If $\displaystyle I_{1}= \int_{0}^{\pi}\frac{x\sin x}{1+\cos^{2} x} dx, I_{2}=\int _{0}^{\pi} x \sin ^{4}x \:dx$ then $I_{1}:I_{2}=$
• A. $3:4$
• B. $1:2$
• C. $2:3$
• D. $4:3$

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Medium
Integrate the function $\frac{1}{\sqrt{(2-x)^2+1}}$

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Medium
$\displaystyle\frac{(x+1)^{2}}{x^{3}+x}=\frac{A}{x}+\frac{Bx+C}{x^{2}+1}\Rightarrow \sin^{-1}[\frac{A}{C}]=$
• A. $\displaystyle\frac{\pi }{4}$
• B. $\displaystyle\frac{\pi }{3}$
• C. $\displaystyle\frac{\pi }{2}$
• D. $\displaystyle\frac{\pi }{6}$

$\int_{}^{} {\frac{{ - 1}}{{\sqrt {1 - {x^2}} }}dx}$