Mathematics

# The integral $\displaystyle\int \dfrac{dx}{x^2(x^4+1)^{3/4}}$ equals?

$\left(\dfrac{x^4+1}{x^4}\right)^{1/4}+C$

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Single Correct Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 86

#### Realted Questions

Q1 Subjective Medium
$\int { \sin ^{ 2 }{ \cfrac { x }{ 2 } } } dx\quad$

1 Verified Answer | Published on 17th 09, 2020

Q2 Multiple Correct Hard
If $\displaystyle \int \frac {xe^x}{\sqrt {1 + e^x}} dx = f(x) \sqrt {1 + e^x} -2 \log \: g(x) + C$, then
• A. $\displaystyle f(x) = x - 1$
• B. $\displaystyle g(x) = \frac {\sqrt {1 + e^x} + 1}{\sqrt {1 + e^x} - 1}$
• C. $\displaystyle g(x) = \frac {\sqrt {1 + e^x} - 1}{\sqrt {1 + e^x} + 1}$
• D. $\displaystyle f(x) = 2(x - 2)$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Medium
$\int_{2}^{3}\dfrac{2-x}{\sqrt{5x-6-x^{2}}} dx =$
• A. $\pi /2$
• B. $-\pi /3$
• C. $\pi$
• D. $-\pi /2$

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Medium
$\int\frac{dx}{x(x^n+1)}$
• A. ${n}$ $(log{x^n}$-$log(x^n +1))+C$
• B. $\frac{1}{n}$ $(log{x^n}$+$log(x^n +1))+C$
• C. ${n}$ $(log{x^n}$+$log(x^n +1))+C$
• D. $\frac{1}{n}$ $(log{x^n}$-$log(x^n +1))+C$

Let $\displaystyle I_{1}=\int_{0}^{1}(1-x^{2})^{1/3} dx$  &  $\displaystyle I_{2}=\int_{0}^{1}(1-x^{3})^{1/2} dx$