Mathematics

# $\displaystyle\int { { e }^{ \sin ^{ 2 }{ x } } } \left( \cos { x } +\cos ^{ 3 }{ x } \right) \sin { x } dx=$

$\dfrac { 1 }{ 2 } { e }^{ \sin ^{ 2 }{ x } }\left( 3-\sin ^{ 2 }{ x } \right) +c$

Its FREE, you're just one step away

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

#### Realted Questions

Q1 Single Correct Medium
The value of $\displaystyle \int_2^4 \left( \dfrac{\log t}{t} \right ) dt$ is
• A. $\dfrac{1}{2} (\log 2)^2$
• B. $\dfrac{5}{2} (\log 2)^2$
• C. $(\log 2)^2$
• D. $\dfrac{3}{2} (\log 2)$
• E. $\dfrac{3}{2} (\log 2)^2$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
(A) : $\displaystyle \int e^{x}(\log x+x^{-2})dx={ e }^{ x }\left( \log x-\frac { 1 }{ x } \right) +c$
(R): $\displaystyle \int e^{x}[f(x)+f'(x)]dx=e^{x}f(x)+c$
• A. Both A and R are true but R is not correct explanation of A
• B. A is true but R is false
• C. A is false but R is true.
• D. Both A and R are true and R is the correct explanation of A

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Hard
If $\displaystyle \int x^{5}(1+x^{3})^{2/3}dx=A(1+x^{3})^{8/3}+B(1+x^{3})^{5/3}+c$, then
• A. $A=\dfrac{1}{8},B=-\dfrac{1}{5}$
• B. $A=-\dfrac{1}{8},B=\dfrac{1}{5}$
• C. None of these
• D. $A=\dfrac{1}{4},B=\dfrac{1}{5}$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
Evaluate the following integrals:
$\int { \sin ^{ 3 }{ x } \cos ^{ 5 }{ x } } dx$

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 $\displaystyle f(x)>0 \forall x \in R$