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

Step-by-step Solution

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Final Answer

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

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Rewrite the expression $\frac{2x^2-x+4}{x^3+4x}$ inside the integral in factored form

$\int\frac{2x^2-x+4}{x\left(x^2+4\right)}dx$

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

$\int\frac{2x^2-x+4}{x\left(x^2+4\right)}dx$

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Learn how to solve integrals by partial fraction expansion problems step by step online. Find the integral int((2x^2-x+4)/(x^3+4x))dx. Rewrite the expression \frac{2x^2-x+4}{x^3+4x} inside the integral in factored form. Rewrite the fraction \frac{2x^2-x+4}{x\left(x^2+4\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 x\left(x^2+4\right). Multiply both sides of the equality by 1 to simplify the fractions.

Final Answer

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

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Function Plot

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

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1
2
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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 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.

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