Mathematics

# Solve $\int {{e^x}\,\cos e{c^2}\,\left( {{e^x}} \right)\,dx}$

##### SOLUTION
$I=\displaystyle\int e^{x}\csc^{2}(e^{x})dx$

Let $e^{x}=t\Rightarrow e^{x}dx=dt$

$I=\displaystyle\int\csc^{2}t dt =-\cot (t)+C$

$=-\cot (e^{x})+C$

$\therefore \displaystyle\int e^{x}\csc^{2} (e^{x})dx=-\cot (e^{x})+C$

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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
If  $\displaystyle I_n=\int_{0}^{\tfrac{\pi}{4}} \tan^nx\sec^2xdx,$ then  $I_1, I_2, I_3..$ are  in
• A. A.P.
• B. G.P.
• C. A.G.P.
• D. H.P.

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
$\displaystyle \int { { e }^{ x }{ \left( \frac { x+2 }{ x+4 } \right) }^{ 2 }dx }$ is equal to
• A. $\displaystyle { e }^{ x }{ \left( \frac { x+2 }{ x+4 } \right) }+c$
• B. $\displaystyle \frac { { e }^{ x } }{ x+4 } +c$
• C. none of these
• D. $\displaystyle \frac { x{ e }^{ x } }{ x+4 } +c$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Medium
$\displaystyle \int(a-a^{nx})dx=$
• A. $\displaystyle ax+\frac { a^{ nx } }{ n\log a } +c$
• B. $\displaystyle ax+\frac { a^{ nx } }{ \log a } +c$
• C. $\displaystyle ax+\frac { a^{ nx+1 } }{ \log a } +c$
• D. $\displaystyle ax- \frac{a^{nx}}{n\log a}+c$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
Solve:$\int \sin 2x \cos 3x dx$

Let $\displaystyle f\left ( x \right )=\frac{\sin 2x \cdot \sin \left ( \dfrac{\pi }{2}\cos x \right )}{2x-\pi }$