Step-by-step Solution

Integrate $\int\left(x-\left(\frac{1}{3}\right)\right)^3dx$ with respect to x

Go!
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
|◻|
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

Step-by-step explanation

Problem to solve:

$\int\left(x-\frac{1}{3}\right)^3dx$

Learn how to solve calculus problems step by step online.

$\begin{matrix}u=x-\frac{1}{3} \\ du=dx\end{matrix}$

Unlock this full step-by-step solution!

Learn how to solve calculus problems step by step online. Calculate the integral of int((x-1*(1/3))^3)dx. Solve the integral \int\left(x-\frac{1}{3}\right)^3dx applying u-substitution. Let u and du be. Substituting u and dx in the integral and simplify. Apply the power rule for integration, \displaystyle\int x^n dx=\frac{x^{n+1}}{n+1}, where n represents a constant function. Substitute u back for it's value, x-\frac{1}{3}.

Final Answer

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

Problem Analysis

$\int\left(x-\frac{1}{3}\right)^3dx$

Main topic:

Calculus

Related formulas:

1. See formulas

Time to solve it:

~ 0.03 seconds