Mathematics

# $\int {x{{\sin }^{ - 1}}xdx}$=?

$\frac{1}{4}{\sin ^{ - 1}}(x)(2x^2 - 1) + \frac{{x\sqrt {1 - {x^2}} }}{4} + c$

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

#### Realted Questions

Q1 Single Correct Hard
$\displaystyle \int { \cfrac { { x }^{ 3 } }{ \sqrt { 1+x^2 } } } dx$
• A. $\sqrt { 1+x } -\cfrac { x }{ 3 } { \left( 1+{ x }^{ 2 } \right) }^{ 3/2 }+c$
• B. $x\sqrt { 1+{ x }^{ 2 } } +\cfrac { 2 }{ 3 } { \left( 1+{ x }^{ 2 } \right) }^{ 3/2 }+c$
• C. ${ x }^{ 2 }\sqrt { 1+{ x }^{ 2 } } -\cfrac { 1 }{ 3 } { \left( 1+{ x }^{ 2 } \right) }^{ 3/2 }+c$
• D. $\dfrac{{ x }^{ 2 }\sqrt { 1+{ x }^{ 2 } }}{3}-\cfrac { 2 }{ 3 } {\sqrt{1+{ x }^{ 2 }} }+c$

1 Verified Answer | Published on 17th 09, 2020

Q2 Subjective Medium
Integrate:
$\frac { 3 x + 5 } { ( x + 1 ) ( x - 2 ) ^ { 2 } } d x$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Medium
What is $\displaystyle \int { \cfrac { \ln { x } }{ x } } dx$ equal to ?
• A. $\cfrac { \left( \ln { x } \right) }{ 2 } +c$ where $c$ is the constant of integration
• B. ${ \left( \ln { x } \right) }^{ 2 }+c$ where $c$ is the constant of integration
• C. None of the above
• D. $\cfrac { { \left( \ln { x } \right) }^{ 2 } }{ 2 } +c$ where $c$ is the constant of integration

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Medium
If $\displaystyle \int \dfrac{x^4 + 1}{x^6 + 1} dx = \tan^{-1} (f(x)) -\dfrac{2}{3} \tan^{-1} (g(x)) + C$, then
• A. $g(x)$ is monotonic function
• B. none of these
• C. None
• D. Both $f(x)$ & $g(x)$ are odd functions

Consider two differentiable functions $f(x), g(x)$ satisfying $\displaystyle 6\int f(x)g(x)dx=x^{6}+3x^{4}+3x^{2}+c$ & $\displaystyle 2 \int \frac {g(x)dx}{f(x)}=x^{2}+c$. where $\displaystyle f(x)>0 \forall x \in R$