Mathematics

# Evaluate: $\displaystyle\int \tan^5\theta d\theta$

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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 Medium
If $f(x)$ is odd function and $f(1)=a$, and $f(x+2)=f(x)+f(2)$ then the value of $f(3)$ is
• A. $6a$
• B. $0$
• C. $9a$
• D. $3a$

1 Verified Answer | Published on 17th 09, 2020

Q2 Subjective Hard
Prove that : $\displaystyle \int_{0}^{1} \tan^{-1} x dx = \dfrac {\pi}{4} - \dfrac {1}{2}\log 2$.

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Medium
$\displaystyle \int { \frac { { x }^{ 2 }-2 }{ { x }^{ 3 }\sqrt { { x }^{ 2 }-1 } } dx }$ is equal to
• A. $\displaystyle \frac { { x }^{ 2 } }{ \sqrt { { x }^{ 2 }-1 } }$
• B. $\displaystyle -\frac { { x }^{ 2 } }{ \sqrt { { x }^{ 2 }-1 } }$
• C. $\displaystyle \frac { \sqrt { { x }^{ 2 }-1 } }{ { x }^{ 2 } }$
• D. $\displaystyle -\frac { \sqrt { { x }^{ 2 }-1 } }{ { x }^{ 2 } }$

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Medium
$\displaystyle \int_{0}^{\infty} \dfrac {x \ln x}{(1 + x^{2})^{2}}dx =$
• A. $1$
• B. $-1$
• C. $\dfrac {\pi}{2}$
• D. $0$

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