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Find the integral $\int\frac{15}{x^2+3x-10}dx$

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Solution

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Final answer to the problem

$\frac{15}{7}\ln\left|x-2\right|-\frac{15}{7}\ln\left|x+5\right|+C_0$
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Learn how to solve integrals by partial fraction expansion problems step by step online. Find the integral int(15/(x^2+3x+-10))dx. Rewrite the expression \frac{15}{x^2+3x-10} inside the integral in factored form. Rewrite the fraction \frac{15}{\left(x-2\right)\left(x+5\right)} in 2 simpler fractions using partial fraction decomposition. Expand the integral \int\left(\frac{15}{7\left(x-2\right)}+\frac{-15}{7\left(x+5\right)}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int\frac{15}{7\left(x-2\right)}dx results in: \frac{15}{7}\ln\left(x-2\right).

Final answer to the problem

$\frac{15}{7}\ln\left|x-2\right|-\frac{15}{7}\ln\left|x+5\right|+C_0$

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Function Plot

Plotting: $\frac{15}{7}\ln\left(x-2\right)-\frac{15}{7}\ln\left(x+5\right)+C_0$

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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

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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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