Mathematics

# Evaluate$\int {\frac{{{x^2}}}{{{x^2} + 1}}dx}$

$x-\tan^{-1}x+C$

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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 Medium
Let  $\theta$  be the angle between the lines  ${ L }_{ { 1 } }:\left[ \begin{array}{l} { { x }=2{ t }+{ 1 } } \\ { { y }={ t }+{ 1 } } \\ { { z }=3{ t }+{ 1 } } \end{array} \right.$  and  ${ L }_{ { 2 } }:\left[ \begin{array}{l} { { x }=3{ s }+2 } \\ { { y }=6{ s }-1 } \\ { { z }=4 } \end{array} \right.$  where  $s , t \in { R }.$  Then the value of  $\int _ { 0 } ^ { \theta } \dfrac { 1 } { 1 + \tan x } d x =$
• A. $\pi / 4$
• B. $\pi / 2$
• C. $\pi / 3$
• D. $\pi / 6$

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
The integral $\displaystyle \int^{4}_{2}\dfrac {\log x^{2}}{\log x^{2}+\log (36-12x+x^{2})}dx$ is equal to
• A. $2$
• B. $4$
• C. $6$
• D. $1$

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Medium
$\displaystyle\int { \dfrac { { x }^{ 5 } }{ \sqrt { 1+{ x }^{ 3 } } } dx }$ is equal to
• A. $\dfrac { 2 }{ 9 } \sqrt { { x }^{ 3 }-9 } \left( 1+{ x }^{ 2 } \right) +C$
• B. $\dfrac { 2 }{ 9 } \sqrt { 1+{ x }^{ 3 } } +C$
• C. $\dfrac { 2 }{ 9 } \sqrt { 1+{ x }^{ 3 } } \left( { x }^{ 3 }-2 \right) +C$
• D. $\dfrac { 2 }{ 9 } \sqrt { 1+{ x }^{ 2 } } \left( { x }^{ 3 }+9 \right) +C$
• E. $\dfrac { 2 }{ 9 } \sqrt { 1+{ x }^{ 2 } } \left( { x }^{ 3 }-9 \right) +C$

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Hard
Evaluate: $\displaystyle\int_{0}^{\dfrac{\pi}{2}}\sqrt{sin\,\phi} \, cos^5\,\phi\,d\,\phi$

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020

Q5 Passage Medium
Let $\displaystyle I_{1}=\int_{0}^{1}(1-x^{2})^{1/3} dx$  &  $\displaystyle I_{2}=\int_{0}^{1}(1-x^{3})^{1/2} dx$

On the basis of above information, answer the following questions:

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020