Mathematics

# $\displaystyle \int{\dfrac{1}{x+\sqrt{x-1}}dx}$=

$\log(x+\sqrt{x-1})+\sin^{-1}\sqrt{\dfrac{x-1}{x}}+c$

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

#### Realted Questions

Q1 Single Correct Medium
$\int ^\pi _0 | cos x|^3 dx$ is equal to
• A. $\dfrac{2}{3}$
• B. $0$
• C. $\dfrac{-8}{3}$
• D. $\dfrac{4}{3}$

1 Verified Answer | Published on 17th 09, 2020

Q2 Subjective Medium
$\displaystyle\int^1_0\cot^{-1}(1+x^2-x)dx$.

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Medium
Simplify the given logarithmic function:
$(x^2+1) \log x$

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Hard
$\displaystyle \int_{0}^{\pi/4}{\dfrac{x.\sin x}{\cos^{3}x}dx}$ equals to :
• A. $\dfrac{\pi}{4}+\dfrac{1}{2}$
• B. $\dfrac{\pi}{4}$
• C. $\dfrac{\pi}{4}+1$
• D. $\dfrac{\pi}{4}-\dfrac{1}{2}$

Solve $\left[-\displaystyle \int^{\pi/2}_0\cos \left(\dfrac{\pi}{4}+\dfrac{x}{2}\right)e^x\right]dx$