Mathematics

# If $I=\int \dfrac{\sin2x}{(3+4\cos x)^3}dx$ then $I$ is equal to

$\dfrac{3+8 \cos x}{16(3+4 \cos x)^2}+C$

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

#### Realted Questions

Q1 Single Correct Hard
The integral $\displaystyle \int (1+x-\displaystyle \frac{1}{x})e^{x+\frac{1}{x}} dx$ is equal to
• A. $(x-1)e^{x+ \frac{1}{x}} +c$
• B. $(x+1)e^{x+\frac{1}{x}} +c$
• C. $-xe^{x+\frac{1}{x}} +c$
• D. $xe^{x+\frac{1}{x}} +c$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
The value of $\displaystyle\int_{-1}^1{\left(\frac{x^2+\sin{x}}{1+x^2}\right)dx}$, is equal to
• A. $2-\pi$
• B. $\pi-2$
• C. none of these
• D. $\displaystyle2-\frac{\pi}{2}$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Medium
Evaluate $\displaystyle \int\frac{\sqrt{1+\sqrt{x}}}{\sqrt{x}}dx$
• A. $\displaystyle \dfrac { 3{ \left( \sqrt { x } +1 \right) }^{ \frac { 4 }{ 3 } } }{ 4 } +c$
• B. $\displaystyle \dfrac { { \left( \sqrt { x } +1 \right) }^{ \frac { 4 }{ 3 } } }{ 4 } +c$
• C. $\displaystyle \dfrac { { \left( \sqrt { x } +1 \right) }^{ \frac { 2 }{ 3 } } }{ 3 } +c$
• D. $\displaystyle \dfrac { 4{ \left( \sqrt { x } +1 \right) }^{ \frac { 3 }{ 2 } } }{ 3 } +c$

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Medium
$\int {\dfrac{{dx}}{{x\left( {{x^n} + 1} \right)}}}$ is equal to
• A. $\frac{1}{n}\log \left( {\frac{{{x^n}}}{{{x^n} + 1}}} \right)$
• B. $\log \left( {\frac{{{x^n}}}{{{x^n} + 1}}} \right)$
• C. None of these
• D. $\frac{1}{n}\log \left( {\frac{{{x^n} + 1}}{{{x^n}}}} \right)$

Evaluate $\displaystyle \int x^{2}e^{x}dx$.