Mathematics

$\int { { e }^{ 3x } } \cdot { x }^{ 2 }dx$

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

Realted Questions

Q1 Subjective Medium
Integrate the function    $\tan^{-1}x$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Hard
The value of $\int {{{(x - 2)} \over {{{\left\{ {{{(x - 2)}^2}{{(x + 3)}^7}} \right\}}^{{1 \over 3}}}}}} dx$ is

• A. ${3 \over {20}}{\left( {{{x - 2} \over {x + 3}}} \right)^{{3 \over 4}}} + c$
• B. ${5 \over {12}}{\left( {{{x - 2} \over {x + 3}}} \right)^{{4 \over 3}}} + c$
• C. ${3 \over {20}}{\left( {{{x - 2} \over {x + 3}}} \right)^{{5 \over 3}}} + c$
• D. ${3 \over {20}}{\left( {{{x - 2} \over {x + 3}}} \right)^{{4 \over 3}}} + c$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Medium
If $\displaystyle \int_0^{\pi} \dfrac{x^2}{(1+\sin \,x)^2} dx = A$ the $\displaystyle \int_0^{\pi} \dfrac{2x^2cos^2(x/2)}{(1+\sin x)^2} dx=$ ?
• A. $A-\pi+ \pi^2$
• B. $A-\pi - \pi^2$
• C. $A+2\pi - \pi^2$
• D. $A+\pi - \pi^2$

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Medium
$\displaystyle \int \sinh^{-1}\left(\frac{x}{4}\right)dx$ is equal to
• A. $x\sinh^{-1} \left(\displaystyle \frac{x}{4}\right)+{\sqrt{x^{2}+16}}+c$
• B. $x\sinh^{-1} {\left(\dfrac{x}{4}\right)-\dfrac{1}{2}}\sqrt{x^{2}+16}+c$
• C. $x\sinh^{-1} {\left(\dfrac{x}{2}\right)-x}\sqrt{x^{2}+16}+c$
• D. $x \sinh^{-1} \left(\displaystyle \frac{x}{4}\right)-\sqrt{x^{2}+16}+c$

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 $\displaystyle f(x)>0 \forall x \in R$