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# Integrate $\int\left(x^2\sqrt{6x^3}+5\right)dx$

## Step-by-step Solution

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$\frac{4}{3\sqrt{6}}\sqrt{x^{9}}+5x+C_0$
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##  Step-by-step Solution 

Problem to solve:

$\int\left(x^2\sqrt{6x^3}+5\right)dx$

Specify the solving method

1

Expand the integral $\int\left(x^2\sqrt{6x^3}+5\right)dx$ into $2$ integrals using the sum rule for integrals, to then solve each integral separately

$\int x^2\sqrt{6x^3}dx+\int5dx$

Learn how to solve integrals with radicals problems step by step online.

$\int x^2\sqrt{6x^3}dx+\int5dx$

Learn how to solve integrals with radicals problems step by step online. Integrate int(x^2(6x^3)^1/2+5)dx. Expand the integral \int\left(x^2\sqrt{6x^3}+5\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int x^2\sqrt{6x^3}dx results in: \frac{4}{3\sqrt{6}}\sqrt{x^{9}}. The integral \int5dx results in: 5x. Gather the results of all integrals.

$\frac{4}{3\sqrt{6}}\sqrt{x^{9}}+5x+C_0$

##  Explore different ways to solve this problem

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a
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x
y
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◻/◻
/
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e
π
ln
log
log
lim
d/dx
Dx
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

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