Mathematics

# Evaluate the following integral:$\int { { e }^{ \cos ^{ 2 }{ x } }\sin { 2x } } dx\quad$

##### SOLUTION
Let
$t={\cos}^{2}{x}\Rightarrow\,dt=-2\cos{x}\sin{x}dx=-\sin{2x}dx$

$\displaystyle\int{{e}^{{\cos}^{2}{x}}\sin{2x}\,dx}$

$=-\displaystyle\int{{e}^{t}\,dt}$

$=-{e}^{t}+c$

$=-{e}^{{\cos}^{2}{x}}+c$ where $t={\cos}^{2}{x}$

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Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 84

#### Realted Questions

Q1 Single Correct Hard
Solve $\displaystyle\int \left(\sqrt{\tan x}+\sqrt{\cot x}\right)dx$.
• A. $I =\sqrt{2}{{\tan }^{-1}}\left( \dfrac{1+\tan x}{\sqrt{2\tan x}} \right)+{{C}_{1}}$
• B. $I ={{\tan }^{-1}}\left( \dfrac{1-\tan x}{\sqrt{2\tan x}} \right)+{{C}_{1}}$
• C. None of these
• D. $I =\sqrt{2}{{\tan }^{-1}}\left( \dfrac{1-\tan x}{\sqrt{2\tan x}} \right)+{{C}_{1}}$

1 Verified Answer | Published on 17th 09, 2020

Q2 Subjective Medium
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Q3 Subjective Medium
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