Mathematics

# $\displaystyle\int \dfrac{(3x^3+1)dx}{x(x\cdot e^{x^3}+1)}$ is equal to?

$ln \left|\dfrac{xe^{x^3}-1}{xe^{x^3}}\right|+C$

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

#### Realted Questions

Q1 Single Correct Medium
If $\displaystyle I = \int \frac {1}{e^x} \tan^{-1} (e^x) dx$, then I equals
• A. $\displaystyle - e^{-x} \tan^{-1} (e^x) + \log (1 + e^{2x}) + C$
• B. $\displaystyle x - e^{-x} \tan^{-1} e^x - \frac {1}{2} \log (1 + e^x) + C$
• C. none of these
• D. $\displaystyle x - e^{-x} \tan^{-1} (e^x) - \frac {1}{2} \log (1 + e^{2x}) + C$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
Let $I={\int}_{0}^{1}\dfrac{\sin x}{\sqrt{x}}dx$ and $J={\int}_{0}^{1}\dfrac{\cos x}{\sqrt{x}}dx$. Then, which one of the following is true?
• A. $I<\dfrac{2}{3}$ and $J<2$
• B. $I<\dfrac{2}{3}$ and $J>2$
• C. $I>\dfrac{2}{3}$ and $J<2$
• D. $I>\dfrac{2}{3}$ and $J>2$

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Medium
$\int {\frac{\cos xdx}{3+4\sin x}}$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Hard
Find the value of A and B,if $\int_{}^{} {\frac{{dx}}{{5 + 4\cos x}}} = A{\tan ^{ - 1}}(B\tan \frac{x}{2}) + c$

1 Verified Answer | Published on 17th 09, 2020

Q5 Single Correct Medium
If $f(x)=\int { \cfrac { dx }{ \sin ^{ 1/2 }{ x } \sin ^{ 7/2 }{ x } } }$, then $f(\cfrac{\pi}{4})-f(0)=$
• A. $2.3$
• B. $2.4$
• C. $2.5$
• D. $2.67$