Mathematics

# Solve $\int {2{x^3}{e^{{x^2}}}}$

$(x^2e^{x^2}-e^{x^2})+C$

##### SOLUTION
$\int { 2{ x }^{ 3 }{ e }^{ { x }^{ 2 } } } dx$
by integration by partly, we have
Let ${ x }^{ 2 }=t$
$\Rightarrow 2xdx=dt$
$\Rightarrow 2\sqrt { t } dx=dt$
$\Rightarrow \int { 2{ x }^{ 2 }.x.{ e }^{ { x }^{ 2 } }dx }$
$\Rightarrow \int { 2t } { e }^{ t }.\dfrac { dt }{ 2 }$
$\Rightarrow \int { t } .{ e }^{ t }dt=t.\int { { e }^{ t }dt } -\int { \dfrac { d }{ dt } \left( t \right) } \int { { e }^{ t }dt }$
$=t.{ e }^{ t }-\int { { e }^{ t } } dt$
$=t.{ e }^{ t }-{ e }^{ t }+c$
$=\left( { x }^{ 2 }.{ e }^{ { x }^{ 2 } }-{ e }^{ { x }^{ 2 } } \right) +c$
Hence, the answer is $\left( { x }^{ 2 }.{ e }^{ { x }^{ 2 } }-{ e }^{ { x }^{ 2 } } \right) +c.$

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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
The value of $\displaystyle \int_{-\pi/2}^{\pi/2}\sin^{10}x(6x^{9}-25x^{7}+4x^{3}-2x) dx$ is equal to?
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• B. $25$
• C. $2$
• D. $0$

1 Verified Answer | Published on 17th 09, 2020

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Solve:$\displaystyle \int {\sqrt{\tan x}+ \sqrt{\cot x}}.dx$

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Solve:
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Let $I={\int}_{0}^{1}\dfrac{\sin x}{\sqrt{x}}dx$ and $J={\int}_{0}^{1}\dfrac{\cos x}{\sqrt{x}}dx$. Then, which one of the following is true?
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Q5 Passage Hard
Let us consider the integral of the following forms
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