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Find the integral $\int\frac{x^2-64}{x^2+64}dx$

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Solution

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Final answer to the problem

$x-16\arctan\left(\frac{x}{8}\right)+C_0$
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Step-by-step Solution

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Learn how to solve integrals of rational functions problems step by step online. Find the integral int((x^2-64)/(x^2+64))dx. Divide x^2-64 by x^2+64. Resulting polynomial. Expand the integral \int\left(1+\frac{-128}{x^2+64}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int1dx results in: x.

Final answer to the problem

$x-16\arctan\left(\frac{x}{8}\right)+C_0$

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Plotting: $x-16\arctan\left(\frac{x}{8}\right)+C_0$

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0
a
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d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
◻2
◻◻
√◻
√

◻√◻
◻√
∞
e
π
ln
log
log◻
lim
d/dx
D□x
∫
∫◻
|◻|
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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Main Topic: Integrals of Rational Functions

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

Used Formulas

See formulas (3)

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