Mathematics

# $\int (e^{a\ln{x}}+e^{x\ln{a}})dx$, where $x>0,\ a>0$

$x^{a+1}+\dfrac{a^{x}}{\ln{a}}+c$

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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
What is $\int \dfrac {dx}{\sqrt {x^{2} - a^{2}}}$ equal to?
where $c$ is the constant of integration.
• A. $\ln \left |\dfrac {x + \sqrt {x^{2} + a^{2}}}{a}\right | + c$
• B. $\ln \left |\dfrac {x - \sqrt {x^{2} + a^{2}}}{a}\right | + c$
• C. $\ln \left |\dfrac {x^{2} + \sqrt {x^{2} + a^{2}}}{a}\right | + c$
• D. None of the above

1 Verified Answer | Published on 17th 09, 2020

Q2 Subjective Medium
$\displaystyle \int e^x(\tan x+\sec ^2 x)dx$

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Medium
Evaluate $\displaystyle\int_{0}^{\pi/4}\sec ^2 x \ dx$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Hard
$\displaystyle\int { \dfrac { dx }{ { e }^{ x }+{ e }^{ -x } } }$ equals

1 Verified Answer | Published on 17th 09, 2020

Q5 Subjective Medium
Evaluate $\int \dfrac {1}{(4x-1)\sqrt {{(4x-1)}^{2}-1}}dx$