Mathematics

# Integrate:$2x^2e^{x^2}$

##### SOLUTION
$2\int { { x }^{ 2 }{ e }^{ { x }^{ 2 } }dx } =2\left[ { x }^{ 2 }\int { { e }^{ { x }^{ 2 } }dx } +\int { \dfrac { d }{ dx } { x }^{ 2 }. } \int { { e }^{ { x }^{ 2 } }dx } \right] dx\quad \text(integration\quad by\quad parts)\\ =\dfrac { 2{ x }^{ 2 }{ e }^{ { x }^{ 2 } } }{ 2x } +2\int { 2x.\dfrac { { e }^{ { x }^{ 2 } } }{ 2x } dx } \\ =x{ e }^{ { x }^{ 2 } }+\dfrac { 2.{ e }^{ { x }^{ 2 } } }{ 2x } +C\\ =\left( \dfrac { { x }^{ 2 }+1 }{ x } \right) { e }^{ { x }^{ 2 } }+C$

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Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 114

#### Realted Questions

Q1 Subjective Medium
Evaluate $\int \dfrac{sec^2x}{cosec^2x}dx$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Hard
$\int \dfrac {dx}{ \sqrt{(x-a)(b-x)}}$
• A. $2 \sin^{-1} \sqrt{\dfrac{x-a}{b-a}} + c$
• B. $\sin^{-1} \sqrt{\dfrac{x-a}{b-a}} + c$
• C. $2 \sin^{-1} \sqrt{\dfrac{x+a}{b-a}} + c$
• D. None of these

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Medium
If $\displaystyle\int _{ 0 }^{ \pi }{ xf\left( \sin ^{ 2 }{ x } +\sec ^{ 2 }{ x } \right) dx } =k \displaystyle\int _{ 0 }^{ { \pi }/{ 2 } }{ f\left( \sin ^{ 2 }{ x } +\sec ^{ 2 }{ x } \right) dx }$, then the value of $k$ is
• A. $\dfrac { \pi }{ 2 }$
• B. $-\dfrac { \pi }{ 2 }$
• C. None of the above
• D. $\pi$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Hard
The value of integral $\int _{ \cfrac { \pi }{ 4 } }^{ \cfrac { 3\pi }{ 4 } }{ \cfrac { x }{ 1+\sin { x } } } dx$ is

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