Mathematics

# The value of $\displaystyle \int { { e }^{ x }\frac { 1+n{ x }^{ n-1 }-{ x }^{ 2n } }{ \left( 1-{ x }^{ n } \right) \sqrt { 1-{ x }^{ 2n } } } dx }$ is

$\displaystyle { e }^{ x }\frac { \sqrt { 1-{ x }^{ 2n } } }{ 1-{ x }^{ n } } +c$

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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 Medium
The value of integratin $\displaystyle \int x\sec^{-1}xdx$ is
• A. $\dfrac{1}{2}x^{2}\sec^{-1}x+\displaystyle \frac{1}{2}\sqrt{x^{2}-1}+c$
• B. $x^{2}\sec^{2}x+\displaystyle \frac{1}{2}\sqrt{x^{2}-1}+c$
• C. $x^{2}\sec^{2}x-\dfrac{1}{2}\sqrt{x^{2}-1}+c$
• D. $\displaystyle \frac{1}{2}x^{2}\sec^{-1}x-\frac{1}{2}\sqrt{x^{2}-1}+c$

1 Verified Answer | Published on 17th 09, 2020

Q2 Subjective Medium
Integrate the following functions w.r.t $X :(5-3x)(2-3x)^{-\dfrac{1}{2}}$

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Medium
Solve:$\int(1-\cos x)cosec^2 x dx=$ ?

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Medium
The value of  $\displaystyle\int_{0}^{\infty }e^{-ax}\sin (bx) \ dx$ equals?
• A. $\displaystyle \frac{1}{a^{^{2}}+b^{2}}$
• B. $\displaystyle \frac{a}{a^{^{2}}+b^{2}}$
• C. $\displaystyle \frac{1}{b}$
• D. $\displaystyle\frac{b}{a^{2}+b^{2}}$

Let $n \space\epsilon \space N$ & the A.M., G.M., H.M. & the root mean square of $n$ numbers $2n+1, 2n+2, ...,$ up to $n^{th}$ number are $A_{n}$, $G_{n}$, $H_{n}$ and $R_{n}$ respectively.