Find the integral $\int\frac{x-2}{x\left(x^2+5x-14\right)}dx$

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Final answer to the problem

$\frac{1}{7}\ln\left|x\right|-\frac{1}{7}\ln\left|x+7\right|+C_0$
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Step-by-step Solution

How should I solve this problem?

  • Integrate by parts
  • Integrate by partial fractions
  • Integrate by substitution
  • Integrate using tabular integration
  • Integrate by trigonometric substitution
  • Weierstrass Substitution
  • Integrate using trigonometric identities
  • Integrate using basic integrals
  • Product of Binomials with Common Term
  • FOIL Method
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1

Factor the trinomial $\left(x^2+5x-14\right)$ finding two numbers that multiply to form $-14$ and added form $5$

$\begin{matrix}\left(-2\right)\left(7\right)=-14\\ \left(-2\right)+\left(7\right)=5\end{matrix}$

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

$\begin{matrix}\left(-2\right)\left(7\right)=-14\\ \left(-2\right)+\left(7\right)=5\end{matrix}$

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Learn how to solve integrals by partial fraction expansion problems step by step online. Find the integral int((x-2)/(x(x^2+5x+-14)))dx. Factor the trinomial \left(x^2+5x-14\right) finding two numbers that multiply to form -14 and added form 5. Rewrite the polynomial as the product of two binomials consisting of the sum of the variable and the found values. Simplifying. Rewrite the fraction \frac{1}{x\left(x+7\right)} in 2 simpler fractions using partial fraction decomposition.

Final answer to the problem

$\frac{1}{7}\ln\left|x\right|-\frac{1}{7}\ln\left|x+7\right|+C_0$

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Function Plot

Plotting: $\frac{1}{7}\ln\left(x\right)-\frac{1}{7}\ln\left(x+7\right)+C_0$

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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.

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