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Find the integral $\int\frac{x-1}{x^2-16}dx$

Step-by-step Solution

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Final Answer

$\frac{3}{8}\ln\left(x-4\right)+\frac{5}{8}\ln\left(x+4\right)+C_0$
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Step-by-step Solution

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Expand the fraction $\frac{x-1}{x^2-16}$ into $2$ simpler fractions with common denominator $x^2-16$

$\int\left(\frac{x}{x^2-16}+\frac{-1}{x^2-16}\right)dx$

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

$\int\left(\frac{x}{x^2-16}+\frac{-1}{x^2-16}\right)dx$

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Learn how to solve integrals of rational functions problems step by step online. Find the integral int((x-1)/(x^2-16))dx. Expand the fraction \frac{x-1}{x^2-16} into 2 simpler fractions with common denominator x^2-16. Expand the integral \int\left(\frac{x}{x^2-16}+\frac{-1}{x^2-16}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int\frac{x}{x^2-16}dx results in: \frac{1}{2}\ln\left(x+4\right)+\frac{1}{2}\ln\left(x-4\right). Gather the results of all integrals.

Final Answer

$\frac{3}{8}\ln\left(x-4\right)+\frac{5}{8}\ln\left(x+4\right)+C_0$

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Function Plot

Plotting: $\frac{3}{8}\ln\left(x-4\right)+\frac{5}{8}\ln\left(x+4\right)+C_0$

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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

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