Find the integral $\int\frac{7x+3}{\left(x+4\right)\left(x-1\right)}dx$

Step-by-step Solution

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Final answer to the problem

$5\ln\left|x+4\right|+2\ln\left|x-1\right|+C_0$
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Step-by-step Solution

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  • Integrate by partial fractions
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Rewrite the fraction $\frac{7x+3}{\left(x+4\right)\left(x-1\right)}$ in $2$ simpler fractions using partial fraction decomposition

Learn how to solve integrals by partial fraction expansion problems step by step online.

$\frac{5}{x+4}+\frac{2}{x-1}$

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Learn how to solve integrals by partial fraction expansion problems step by step online. Find the integral int((7x+3)/((x+4)(x-1)))dx. Rewrite the fraction \frac{7x+3}{\left(x+4\right)\left(x-1\right)} in 2 simpler fractions using partial fraction decomposition. Expand the integral \int\left(\frac{5}{x+4}+\frac{2}{x-1}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int\frac{5}{x+4}dx results in: 5\ln\left(x+4\right). The integral \int\frac{2}{x-1}dx results in: 2\ln\left(x-1\right).

Final answer to the problem

$5\ln\left|x+4\right|+2\ln\left|x-1\right|+C_0$

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Function Plot

Plotting: $5\ln\left(x+4\right)+2\ln\left(x-1\right)+C_0$

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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 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.

Used Formulas

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