Find the integral $\int\frac{3x-2}{x^2+1\cdot -2x}dx$

Step-by-step Solution

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Final answer to the problem

$\ln\left|x\right|+2\ln\left|x-2\right|+C_0$
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Step-by-step Solution

How should I solve this problem?

  • Integrate by partial fractions
  • Integrate by substitution
  • Integrate by parts
  • 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
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1

Simplifying

$\int\frac{3x-2}{x^2-2x}dx$

Learn how to solve integrals by partial fraction expansion problems step by step online.

$\int\frac{3x-2}{x^2-2x}dx$

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Learn how to solve integrals by partial fraction expansion problems step by step online. Find the integral int((3x-2)/(x^2+1*-2x))dx. Simplifying. Rewrite the expression \frac{3x-2}{x^2-2x} inside the integral in factored form. Rewrite the fraction \frac{3x-2}{x\left(x-2\right)} in 2 simpler fractions using partial fraction decomposition. Expand the integral \int\left(\frac{1}{x}+\frac{2}{x-2}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately.

Final answer to the problem

$\ln\left|x\right|+2\ln\left|x-2\right|+C_0$

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Function Plot

Plotting: $\ln\left(x\right)+2\ln\left(x-2\right)+C_0$

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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 by Partial Fraction Expansion

The partial fraction decomposition or partial fraction expansion of a rational function is the operation that consists in expressing the fraction as a sum of a polynomial (possibly zero) and one or several fractions with a simpler denominator.

Used Formulas

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