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Find the integral $\int\frac{10}{\left(x-1\right)\sqrt{\left(x-1\right)^{\frac{3}{2}}}}dx$

Step-by-step Solution

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Final answer to the problem

$\frac{-40}{3\sqrt[4]{\left(x-1\right)^{3}}}+C_0$
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Step-by-step Solution

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Simplifying

$\int\frac{10}{\left(x-1\right)\sqrt{\sqrt{\left(x-1\right)^{3}}}}dx$

Learn how to solve definition of derivative problems step by step online.

$\int\frac{10}{\left(x-1\right)\sqrt{\sqrt{\left(x-1\right)^{3}}}}dx$

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Learn how to solve definition of derivative problems step by step online. Find the integral int(10/((x-1)(x-1)^(3/2)^1/2))dx. Simplifying. Simplify the expression inside the integral. We can solve the integral \int\frac{10}{\sqrt[4]{\left(x-1\right)^{7}}}dx 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 x-1 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.

Final answer to the problem

$\frac{-40}{3\sqrt[4]{\left(x-1\right)^{3}}}+C_0$

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Function Plot

Plotting: $\frac{-40}{3\sqrt[4]{\left(x-1\right)^{3}}}+C_0$

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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: Definition of Derivative

Resolution of derivatives using the definition of the derivative, which is the limit of difference quotients of real numbers.

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