Mathematics

# $\int_{}^{} {\frac{{dx}}{{x\left( {{x^n} + 1} \right)}}}$ is equal to

$-\frac{1}{n}\log \left( {\frac{{{x^n} + 1}}{{{x^n}}}} \right) + c$

Its FREE, you're just one step away

Single Correct Hard Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 111

#### Realted Questions

Q1 Subjective Medium
Evaluate $\displaystyle\int^{e^2}_e\left\{\dfrac{1}{(log x)}-\dfrac{1}{(log x)^2}\right\}dx$.

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
The value of $\displaystyle \int_0^1 \sqrt{x} \cdot e^{\sqrt{x}} dx$ is equal to
• A. $\dfrac {(e-2)}{2}$
• B. $2e-1$
• C. $2 (e-1)$
• D. $\dfrac {e-1}{2}$
• E. $2 ( e-2)$

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Hard
Evaluate
$\displaystyle \int^{\dfrac{\pi}{2}}_0\dfrac{\sin x}{\sin x+\cos x}dx$

1 Verified Answer | Published on 17th 09, 2020

Q4 Assertion & Reason Hard
##### ASSERTION

$\displaystyle \int_{0}^{1/8}\frac{dx}{1+\left ( \cot 4\pi x \right )^{\sqrt{2}}}=\frac{1}{8}$

##### REASON

If $\displaystyle a+b=\frac{\pi }{2}$, then $\displaystyle \int_{a}^{b}\frac{f\left ( \sin x \right )dx}{f\left ( \sin x \right )+f\left ( \cos x \right )}=\frac{b-a}{2}$

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Assertion is incorrect but Reason is correct

1 Verified Answer | Published on 17th 09, 2020

Q5 Single Correct Medium
Evaluate $\int\limits_1^3 {3{x^2} + 2x + 1} dx$
• A. $24$
• B. $42$
• C. $48$
• D. $36$