Math virtual assistant

About Snapxam Calculators Topics Go Premium
ENGESP
Go!
1
2
3
4
5
6
7
8
9
0
x
y
(◻)
◻/◻
2

e
π
ln
log
lim
d/dx
d/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

\int\frac{x}{\sqrt{5+4x}}dx

Integral of x/((5+4x)^0.5)

Answer

$\frac{1}{8}\left(\frac{\sqrt{\left(4x+5\right)^{3}}}{3}-5\sqrt{4x+5}\right)+C_0$

Step-by-step explanation

Problem

$\int\frac{x}{\sqrt{5+4x}}dx$
1

Solve the integral $\int\frac{x}{\sqrt{4x+5}}dx$ applying u-substitution. Let $u$ and $du$ be

$\begin{matrix}u=\sqrt{4x+5} \\ du=2\left(4x+5\right)^{-\frac{1}{2}}dx\end{matrix}$

Unlock this step-by-step solution!

Answer

$\frac{1}{8}\left(\frac{\sqrt{\left(4x+5\right)^{3}}}{3}-5\sqrt{4x+5}\right)+C_0$
$\int\frac{x}{\sqrt{5+4x}}dx$

Main topic:

Integration by substitution

Used formulas:

6. See formulas

Time to solve it:

~ 1.05 seconds