# Step-by-step Solution

## Integral of $\frac{7x^2-x+16}{x^3+4x}$ with respect to x

Go!
1
2
3
4
5
6
7
8
9
0
x
y
(◻)
◻/◻
÷
2

e
π
ln
log
log
lim
d/dx
Dx
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

### Videos

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

## Step-by-step explanation

Problem to solve:

$\int\:\frac{7x^2-x+16}{x^3+4x}dx$
1

Split the fraction $\frac{7x^2+-x+16}{x^3+4x}$ in two terms with common denominator ($x^3+4x$)

$\int\left(\frac{7x^2}{x^3+4x}+\frac{-x+16}{x^3+4x}\right)dx$
2

Split the fraction $\frac{-x+16}{x^3+4x}$ in two terms with common denominator $x^3+4x$

$\int\left(\frac{7x^2}{x^3+4x}+\frac{-x}{x^3+4x}+\frac{16}{x^3+4x}\right)dx$

$-\frac{1}{2}arctan\left(\frac{1}{2}x\right)+4\ln\left|x\right|+\frac{3}{2}\ln\left|x^{2}+4\right|+C_0$
$\int\:\frac{7x^2-x+16}{x^3+4x}dx$