Mathematics

# $\int { \frac { e\sqrt { x } }{ \sqrt { x } } } \left( x+\sqrt { x } \right)$ dx is equal to:

${ 2e }^{ \sqrt { x } }\left[ x-\sqrt { x}+1 \right] +c$

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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 Hard
Evaluate the given integral.
$\displaystyle\quad \int { \cfrac { x }{ ({ x }^{ 2 }-{ a }^{ 2 })({ x }^{ 2 }-{ b }^{ 2 }) } } dx\quad$

1 Verified Answer | Published on 17th 09, 2020

Q2 Subjective Medium
Evaluate the following : $\displaystyle\int \dfrac{1}{\sqrt{3x^{2}-8}}.dx$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Medium
If $\displaystyle \frac{x^{3}}{(2x-1)(x+2)(x-3)} =$ $A+\displaystyle \frac{B}{(2x-1)}+\frac{C}{(x+2)}+\frac{D}{(x-3)}$ then $\mathrm{A}=$
• A. $\displaystyle \frac{-1}{50}$
• B. $\displaystyle \frac{-8}{25}$
• C. $\displaystyle \frac{27}{25}$
• D. $\displaystyle \frac{1}{2}$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
Evaluate $\int \sin^{3} x \cos^{3} xdx$

Prove that: $\displaystyle \int \sqrt {a^{2} - x^{2}}dx = \dfrac {x}{2}\sqrt {a^{2} - x^{2}} + \dfrac {a^{2}}{2}\sin^{-1} \left (\dfrac {x}{a}\right ) + c$