Mathematics

# $\displaystyle \int{\dfrac{1-\tan x}{1+\tan x}dx}$ equals-

$\log(\cos x+\sin x)+C$

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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
Find $\int \left(1-\frac{1}{x^2}\right)e^{(x+\frac{1}{x}) }dx$ on I where $I= (0, \infty ).$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Hard
If $\displaystyle \int x\frac{\ln (x+\sqrt{1+x^{2}})}{\sqrt{1+x^{2}}}dx=a\sqrt{1+x^{2}}\:\ln (x+\sqrt{1+x^{2}})+bx+c$, then
• A. $a=1, b=1$
• B. $a=-1, b=1$
• C. $a=-1, b=-1$
• D. $a=1, b=-1$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Medium
Find Integrals of given function: $\int_{}^{} {\tan \theta } {\tan ^2}\theta {\sec ^2}\theta d\theta$
• A. $\dfrac{2\tan^4\theta}{4}+c$
• B. $\dfrac{\tan^4\theta}{8}+c$
• C. None of these
• D. $\dfrac{\tan^4\theta}{4}+c$

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Medium
If $\displaystyle \int \dfrac{x^3-8}{x^3\sqrt{x^4-x^3+2}}dx=\dfrac{k.\sqrt{x^4-x^3+2}}{x^2}+C$, then the value of $k$ is (where $C$ is constant of integration)
• A. $2$
• B. $7$
• C. $4$
• D. $3$

$\underset {n\rightarrow \infty}{lim}\dfrac{1^2+2^2+3^2+.....+n^2}{n^3}=.................$