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

Step-by-step Solution

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Final Answer

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

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We could not solve this problem by using the method: Integrals by Partial Fraction Expansion

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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.

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

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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.

Final Answer

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

Explore different ways to solve this problem

Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

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Function Plot

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

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5
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7
8
9
0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
2

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

How to improve your answer:

Main Topic: Integrals with Radicals

Integrals with radicals are those integrals that contain a radical (square root, cubic, etc.) in the numerator or denominator of the integral.

Used Formulas

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