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Find the integral $\int\frac{x^2}{x-1}dx$

Step-by-step Solution

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ln
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log
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sin
cos
tan
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asin
acos
atan
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asec
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sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

Final answer to the problem

$\frac{1}{2}x^2+x+\ln\left|x-1\right|+C_0$
Got another answer? Verify it here!

Step-by-step Solution

How should I solve this problem?

  • Integrate by parts
  • Integrate by partial fractions
  • Integrate by substitution
  • Integrate using tabular integration
  • Integrate by trigonometric substitution
  • Weierstrass Substitution
  • Integrate using trigonometric identities
  • Integrate using basic integrals
  • Product of Binomials with Common Term
  • FOIL Method
  • Load more...
Can't find a method? Tell us so we can add it.
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Rewrite the fraction $\frac{x^2}{x-1}$ inside the integral as the product of two functions: $x^2\frac{1}{x-1}$

$\int x^2\frac{1}{x-1}dx$

Learn how to solve trigonometric integrals problems step by step online.

$\int x^2\frac{1}{x-1}dx$

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Learn how to solve trigonometric integrals problems step by step online. Find the integral int((x^2)/(x-1))dx. Rewrite the fraction \frac{x^2}{x-1} inside the integral as the product of two functions: x^2\frac{1}{x-1}. We can solve the integral \int x^2\frac{1}{x-1}dx by applying integration by parts method to calculate the integral of the product of two functions, using the following formula. First, identify or choose u and calculate it's derivative, du. Now, identify dv and calculate v.

Final answer to the problem

$\frac{1}{2}x^2+x+\ln\left|x-1\right|+C_0$

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Function Plot

Plotting: $\frac{1}{2}x^2+x+\ln\left|x-1\right|+C_0$

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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: Trigonometric Integrals

Integrals that contain trigonometric functions and their powers.

Used Formulas

See formulas (1)

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