Mathematics

# In $I_n=\displaystyle\int (ln x)^ndx$, then $I_n+nI_{n-1}=?$

$x(ln x)^n+C$

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

#### Realted Questions

Q1 Subjective Medium
Solve :
$\int \cos (log x)dx$ ?

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Hard
The value of $\smallint {\textstyle{1 \over {x + \sqrt {x - 1} }}}$ dx is
• A. $\log \left( {x + \sqrt {x - 1} } \right) + {\sin ^{ - 1}}\sqrt {\frac{{x - 1}}{x}} + C$
• B. $\log \left( {x + \sqrt {x - 1} } \right) + C$
• C. none of these
• D. $\log \left( {x + \sqrt {x - 1} } \right) - \frac{2}{3}{\tan ^{ - 1}}\left\{ {\frac{{2\sqrt {x - 1} + 1}}{{\sqrt 3 }}} \right\}C$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Medium
Area enclosed by $x^2 = 4y$ and $y=\frac{8}{x^2 + 4}$ is
• A. $\pi - \frac{2}{3}$
• B. $\pi - \frac{1}{3}$
• C. None of these
• D. $2\pi - \frac{4}{3}$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Hard
Integrate w.r.t $x$:$\dfrac{dx}{{\left({\sin}^{3}{x}{\cos}^{5}{x}\right)}^{\frac{1}{4}}}$

Consider two differentiable functions $f(x), g(x)$ satisfying $\displaystyle 6\int f(x)g(x)dx=x^{6}+3x^{4}+3x^{2}+c$ & $\displaystyle 2 \int \frac {g(x)dx}{f(x)}=x^{2}+c$. where $\displaystyle f(x)>0 \forall x \in R$