Mathematics

# $\int {x\left( {\frac{{\ln {a^{{a^{\frac{x}{2}}}}}}}{{3{a^{\frac{{5x}}{2}}}{b^{3x}}}} + \frac{{\ln {b^{{b^{\frac{x}{2}}}}}}}{{2{a^{2x}}{b^{4x}}}}} \right)} dx\left( {where\,a,b \in R} \right)$ is equal to

$\frac{1}{{6\ln {a^2}{b^3}}}\frac{1}{{{a^{2x}}{b^{3x}}}}\ln \left( {e{a^{2x}}{b^{3x}}} \right) + k$

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

#### Realted Questions

Q1 Subjective Medium
If $P(n)$ is the statement $"n^2$ is even", then what is $P(3)$?

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
$I$ : $\displaystyle \int e^{x}(1-\cot x+\cot^{2}x)dx=-e^{x}\cot x+c$

$\displaystyle II:\int e^{x}(\frac{1+x\log x}{x})dx=e^{x}\log x+c$
• A. only I is true
• B. only II is true
• C. neither I nor II are true
• D. both I and II are true

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Medium
$\displaystyle \int \dfrac{x^3}{x + 1}$ is equal to
• A. $x + \dfrac{x^2}{2} + \dfrac{x^3}{3} - log |1 - x| + C$
• B. $x + \dfrac{x^2}{2} - \dfrac{x^3}{3} - log |1 - x| + C$
• C. $x - \dfrac{x^2}{2} - \dfrac{x^3}{3} - log |1 + x| + C$
• D. $x - \dfrac{x^2}{2} - \dfrac{x^3}{3} - log |1 + x| + C$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
Find : $\displaystyle \int \dfrac{sin^2x - cos^2 x}{sin\, x\,cos\, x} dx$

$\int(2x^2-3 \, sin x+5 \sqrt{x})dx$