Math virtual assistant

Calculators Topics Go Premium About Snapxam
ENGESP

Step-by-step Solution

Integral of $\int\sqrt{x}\left(\sqrt{x}+3\right)dx$

Go!
1
2
3
4
5
6
7
8
9
0
x
y
(◻)
◻/◻
÷
2

e
π
ln
log
log
lim
d/dx
Dx
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

Answer

$\frac{1}{2}x^{2}+2\sqrt{x^{3}}+C_0$

Step-by-step explanation

Problem to solve:

$\int\sqrt{x}\left(\sqrt{x}\:+3\:\right)dx$
1

Solve the integral $\int\sqrt{x}\left(\sqrt{x}+3\right)dx$ applying u-substitution. Let $u$ and $du$ be

$\begin{matrix}u=\sqrt{x} \\ du=\frac{1}{2}x^{-\frac{1}{2}}dx\end{matrix}$
2

Isolate $dx$ in the previous equation

$\frac{du}{\frac{1}{2}x^{-\frac{1}{2}}}=dx$

Unlock this step-by-step solution!

Answer

$\frac{1}{2}x^{2}+2\sqrt{x^{3}}+C_0$