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Find the integral $\int\frac{2x^2-x-20}{x^2+x-6}dx$

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Solution

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Final answer to the problem

$2x-\frac{14}{5}\ln\left|x-2\right|-\frac{1}{5}\ln\left|x+3\right|+C_0$
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Learn how to solve integrals of rational functions problems step by step online. Find the integral int((2x^2-x+-20)/(x^2+x+-6))dx. Rewrite the expression \frac{2x^2-x-20}{x^2+x-6} inside the integral in factored form. Expand. Divide 2x^2-x-20 by x^2+x-6. Resulting polynomial.

Final answer to the problem

$2x-\frac{14}{5}\ln\left|x-2\right|-\frac{1}{5}\ln\left|x+3\right|+C_0$

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Function Plot

Plotting: $2x-\frac{14}{5}\ln\left(x-2\right)-\frac{1}{5}\ln\left(x+3\right)+C_0$

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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
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

How to improve your answer:

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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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