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Find the integral $\int\frac{3x^3-8x^2+10}{x\left(x-1\right)^3}dx$

Step-by-step Solution

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Final Answer

$-10\ln\left(x\right)+\frac{-5}{2\left(x-1\right)^{2}}+13\ln\left(x-1\right)+\frac{12}{x-1}+C_0$
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Step-by-step Solution

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Rewrite the fraction $\frac{3x^3-8x^2+10}{x\left(x-1\right)^3}$ in $4$ simpler fractions using partial fraction decomposition

$\frac{3x^3-8x^2+10}{x\left(x-1\right)^3}=\frac{A}{x}+\frac{B}{\left(x-1\right)^3}+\frac{C}{x-1}+\frac{D}{\left(x-1\right)^{2}}$

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$\frac{3x^3-8x^2+10}{x\left(x-1\right)^3}=\frac{A}{x}+\frac{B}{\left(x-1\right)^3}+\frac{C}{x-1}+\frac{D}{\left(x-1\right)^{2}}$

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Learn how to solve problems step by step online. Find the integral int((3x^3-8x^2+10)/(x(x-1)^3))dx. Rewrite the fraction \frac{3x^3-8x^2+10}{x\left(x-1\right)^3} in 4 simpler fractions using partial fraction decomposition. Find the values for the unknown coefficients: A, B, C, D. The first step is to multiply both sides of the equation from the previous step by x\left(x-1\right)^3. Multiply both sides of the equality by 1 to simplify the fractions. Multiplying polynomials.

Final Answer

$-10\ln\left(x\right)+\frac{-5}{2\left(x-1\right)^{2}}+13\ln\left(x-1\right)+\frac{12}{x-1}+C_0$

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Function Plot

Plotting: $-10\ln\left(x\right)+\frac{-5}{2\left(x-1\right)^{2}}+13\ln\left(x-1\right)+\frac{12}{x-1}+C_0$

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7
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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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