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

Step-by-step Solution

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Final Answer

$-\frac{1}{6}\ln\left(x+1\right)+\frac{2}{3}\ln\left(x-2\right)-\frac{1}{2}\ln\left(x-1\right)+C_0$
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Step-by-step Solution

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Rewrite the expression $\frac{x}{\left(x^2-1\right)\left(x-2\right)}$ inside the integral in factored form

$\int\frac{x}{\left(x+1\right)\left(x-2\right)\left(x-1\right)}dx$

Learn how to solve differential calculus problems step by step online.

$\int\frac{x}{\left(x+1\right)\left(x-2\right)\left(x-1\right)}dx$

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Learn how to solve differential calculus problems step by step online. Find the integral int(x/((x^2-1)(x-2)))dx. Rewrite the expression \frac{x}{\left(x^2-1\right)\left(x-2\right)} inside the integral in factored form. Rewrite the fraction \frac{x}{\left(x+1\right)\left(x-2\right)\left(x-1\right)} in 3 simpler fractions using partial fraction decomposition. Find the values for the unknown coefficients: A, B, C. The first step is to multiply both sides of the equation from the previous step by \left(x+1\right)\left(x-2\right)\left(x-1\right). Multiplying polynomials.

Final Answer

$-\frac{1}{6}\ln\left(x+1\right)+\frac{2}{3}\ln\left(x-2\right)-\frac{1}{2}\ln\left(x-1\right)+C_0$

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Function Plot

Plotting: $-\frac{1}{6}\ln\left(x+1\right)+\frac{2}{3}\ln\left(x-2\right)-\frac{1}{2}\ln\left(x-1\right)+C_0$

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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

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Main Topic: Differential Calculus

The derivative of a function of a real variable measures the sensitivity to change of a quantity (a function value or dependent variable) which is determined by another quantity (the independent variable). Derivatives are a fundamental tool of calculus.

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