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Find the integral $\int\frac{2x^4}{x^3-x^2+x-1}dx$

Step-by-step Solution

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Final Answer

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

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1

Take out the constant $2$ from the integral

$2\int\frac{x^4}{x^3-x^2+x-1}dx$

Learn how to solve integrals of rational functions problems step by step online.

$2\int\frac{x^4}{x^3-x^2+x-1}dx$

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Learn how to solve integrals of rational functions problems step by step online. Find the integral int((2x^4)/(x^3-x^2x+-1))dx. Take out the constant 2 from the integral. Divide x^4 by x^3-x^2+x-1. Resulting polynomial. Expand the integral \int\left(x+1+\frac{1}{x^3-x^2+x-1}\right)dx into 3 integrals using the sum rule for integrals, to then solve each integral separately.

Final Answer

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

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Function Plot

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

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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: Integrals of Rational Functions

Integrals of rational functions of the form R(x) = P(x)/Q(x).

Used Formulas

5. See formulas

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