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# Find the integral $\int\left(5x-5\right)^5dx$

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##  Final Answer

$\frac{1}{30}\left(5x-5\right)^{6}+C_0$
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##  Step-by-step Solution 

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We can solve the integral $\int\left(5x-5\right)^5dx$ by applying integration by substitution method (also called U-Substitution). First, we must identify a section within the integral with a new variable (let's call it $u$), which when substituted makes the integral easier. We see that $5x-5$ it's a good candidate for substitution. Let's define a variable $u$ and assign it to the choosen part

$u=5x-5$

Learn how to solve simplification of algebraic expressions problems step by step online.

$u=5x-5$

Learn how to solve simplification of algebraic expressions problems step by step online. Find the integral int((5x-5)^5)dx. We can solve the integral \int\left(5x-5\right)^5dx by applying integration by substitution method (also called U-Substitution). First, we must identify a section within the integral with a new variable (let's call it u), which when substituted makes the integral easier. We see that 5x-5 it's a good candidate for substitution. Let's define a variable u and assign it to the choosen part. Now, in order to rewrite dx in terms of du, we need to find the derivative of u. We need to calculate du, we can do that by deriving the equation above. Isolate dx in the previous equation. Substituting u and dx in the integral and simplify.

##  Final Answer

$\frac{1}{30}\left(5x-5\right)^{6}+C_0$

##  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

Solve integral of ((5x-5)^5)dx using partial fractionsSolve integral of ((5x-5)^5)dx using basic integralsSolve integral of ((5x-5)^5)dx using u-substitutionSolve integral of ((5x-5)^5)dx using integration by partsSolve integral of ((5x-5)^5)dx using trigonometric substitution

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1
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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

### Main Topic: Simplification of algebraic expressions

The simplification of algebraic expressions consists in rewriting a long and complex expression in an equivalent, but much simpler expression. This simplification can be accomplished through the combined use of arithmetic and algebra rules.

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