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

Step-by-step Solution

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Final Answer

$\ln\left(x-1\right)-2\ln\left(\frac{\frac{\sqrt{3}}{2}}{\sqrt{\frac{3}{4}+\left(x+\frac{1}{2}\right)^2}}\right)+\frac{4\sqrt{3}}{3}\arctan\left(1.154696\left(x+\frac{1}{2}\right)\right)+C_0$
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Step-by-step Solution

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Rewrite the expression $\frac{3x^2+2x-2}{x^3-1}$ inside the integral in factored form

$\int\frac{3x^2+2x-2}{\left(x-1\right)\left(x^2+x+1\right)}dx$

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$\int\frac{3x^2+2x-2}{\left(x-1\right)\left(x^2+x+1\right)}dx$

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Learn how to solve problems step by step online. Find the integral int((3x^2+2x+-2)/(x^3-1))dx. Rewrite the expression \frac{3x^2+2x-2}{x^3-1} inside the integral in factored form. Rewrite the fraction \frac{3x^2+2x-2}{\left(x-1\right)\left(x^2+x+1\right)} in 2 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+x+1\right). Multiply both sides of the equality by 1 to simplify the fractions.

Final Answer

$\ln\left(x-1\right)-2\ln\left(\frac{\frac{\sqrt{3}}{2}}{\sqrt{\frac{3}{4}+\left(x+\frac{1}{2}\right)^2}}\right)+\frac{4\sqrt{3}}{3}\arctan\left(1.154696\left(x+\frac{1}{2}\right)\right)+C_0$

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Function Plot

Plotting: $\ln\left(x-1\right)-2\ln\left(\frac{\frac{\sqrt{3}}{2}}{\sqrt{\frac{3}{4}+\left(x+\frac{1}{2}\right)^2}}\right)+\frac{4\sqrt{3}}{3}\arctan\left(1.154696\left(x+\frac{1}{2}\right)\right)+C_0$

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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

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