Mathematics

# $\displaystyle\int e^{\sin x}\cdot\left(\begin{matrix} \dfrac{sin x+1}{sec x}\end{matrix}\right)dx$ is equal to?

$\sin x\cdot e^{\sin x}+c$

##### SOLUTION
$\displaystyle\int e^{\sin x}(\sin x\cos x+\cos x)dx$

We know $\displaystyle\int e^{g(x)}(g'(x)f(x)+f'(x))dx=e^{g(x)}\cdot f(x)+c$

Here $f(x)=g(x)=\sin x$ and $f'(x)=g'(x)=\cos x$

$=e^{\sin x}\cdot \sin x+c$.

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

#### Realted Questions

Q1 Subjective Medium
Solve: $\displaystyle \int \dfrac{(x^4 - x)^{1/4}}{x^5}dx.$

1 Verified Answer | Published on 17th 09, 2020

Q2 Subjective Hard
Evaluate:
$\int { \cfrac { dx }{ { \left( x+1 \right) }^{ 2 }({ x }^{ 2 }+1) } }$

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Medium
Integrate the following function with respect to $x$
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1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Hard
$\displaystyle \int { \frac { { x }^{ 2 }-8x+7 }{ { \left( { x }^{ 2 }-3x-10 \right) }^{ 2 } } dx } =P\log { \left| x-5 \right| } +Q\frac { 1 }{ x-5 } -R.\log { \left| x+2 \right| } -S.\frac { 1 }{ x+2 } +c$. Then
• A. $\displaystyle P=-\frac { 45 }{ 98 }$
• B. $\displaystyle Q=\frac { 8 }{ 49 }$
• C. $\displaystyle R=\frac { 15 }{ 49 }$
• D. All of these

Consider two differentiable functions $f(x), g(x)$ satisfying $\displaystyle 6\int f(x)g(x)dx=x^{6}+3x^{4}+3x^{2}+c$ & $\displaystyle 2 \int \frac {g(x)dx}{f(x)}=x^{2}+c$. where $\displaystyle f(x)>0 \forall x \in R$