Mathematics

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

##### SOLUTION
$\quad \int { \left( 2{ x }^{ 2 }-3\sin { x } +5\sqrt { x } \right) dx } \\ =\frac { 2{ x }^{ 3 } }{ 3 } +3\cos { x } +\frac { 5{ x }^{ \frac { 3 }{ 2 } } }{ \frac { 3 }{ 2 } } +C\\ =\frac { 2{ x }^{ 3 } }{ 3 } +3\cos { x } +\frac { 10{ x }^{ \frac { 3 }{ 2 } } }{ 3 } +C$

Its FREE, you're just one step away

Subjective Easy Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 111

#### Realted Questions

Q1 Subjective Medium
Find the value of $\displaystyle \int_{0}^{(\pi/2)^{1/3}} x^{5}.\sin x^{3}\ dx$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Hard
Evaluate: $\displaystyle \int \frac{(x^2 - 1)dx}{x^3(\sqrt{2x^4 - 2x^2 + 1})}$
• A. $\sqrt{2 - \dfrac{2}{x^2} + \dfrac{1}{x^4}} + c$
• B. $2\sqrt{2 - \dfrac{2}{x^2} + \dfrac{1}{x^4}} + c$
• C. None of these
• D. $\dfrac{1}{2} \sqrt{2 - \dfrac{2}{x^2} + \dfrac{1}{x^4}} + c$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Medium
Evaluate $\displaystyle \int { \cfrac { 1 }{ \sqrt { x+3 } -\sqrt { x } } } dx$
• A. $\cfrac{2}{3}{(x+2)}^{3/2}+\cfrac{2}{3}x^{3/2}$
• B. $\cfrac{2}{9}{(x+3)}^{3/2}+\cfrac{2}{9}x$
• C. $\cfrac{2}{9}{(x+2)}^{1/2}+\cfrac{2}{9}x^{1/2}$
• D. $\cfrac{2}{9}{(x+3)}^{3/2}+\cfrac{2}{9}x^{3/2}$

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Medium
What is $\int _{ -\frac{\pi}{2} }^{ \frac{\pi}{2}}{ |\sin x| } dx$ equal to ?
• A. 1
• B. $\pi$
• C.
• D. 2

1 Verified Answer | Published on 17th 09, 2020

Q5 Passage Hard
Let us consider the integral of the following forms
$f{(x_1,\sqrt{mx^2+nx+p})}^{\tfrac{1}{2}}$
Case I If $m>0$, then put $\sqrt{mx^2+nx+C}=u\pm x\sqrt{m}$
Case II If $p>0$, then put $\sqrt{mx^2+nx+C}=u\pm \sqrt{p}$
Case III If quadratic equation $mx^2+nx+p=0$ has real roots $\alpha$ and $\beta$, then put $\sqrt{mx^2+nx+p}=(x-\alpha)u\:or\:(x-\beta)u$