Integrate $\int x\sqrt{x}dx$

Step-by-step Solution

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acosh
atanh
acoth
asech
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Final answer to the problem

$\frac{2\sqrt{x^{5}}}{5}+C_0$
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Step-by-step Solution

How should I solve this problem?

  • Integrate by trigonometric substitution
  • Integrate by partial fractions
  • Integrate by substitution
  • Integrate by parts
  • Integrate using tabular integration
  • Weierstrass Substitution
  • Integrate using trigonometric identities
  • Integrate using basic integrals
  • Product of Binomials with Common Term
  • FOIL Method
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1

When multiplying exponents with same base you can add the exponents: $x\sqrt{x}$

$\int\sqrt{x^{3}}dx$

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

$\int\sqrt{x^{3}}dx$

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Unlock the first 3 steps of this solution

Learn how to solve integrals with radicals problems step by step online. Integrate int(xx^(1/2))dx. When multiplying exponents with same base you can add the exponents: x\sqrt{x}. Apply the power rule for integration, \displaystyle\int x^n dx=\frac{x^{n+1}}{n+1}, where n represents a number or constant function, such as \frac{3}{2}. Divide fractions \frac{\sqrt{x^{5}}}{\frac{5}{2}} with Keep, Change, Flip: a\div \frac{b}{c}=\frac{a}{1}\div\frac{b}{c}=\frac{a}{1}\times\frac{c}{b}=\frac{a\cdot c}{b}. As the integral that we are solving is an indefinite integral, when we finish integrating we must add the constant of integration C.

Final answer to the problem

$\frac{2\sqrt{x^{5}}}{5}+C_0$

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Function Plot

Plotting: $\frac{2\sqrt{x^{5}}}{5}+C_0$

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1
2
3
4
5
6
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

See formulas (1)

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