Math virtual assistant

About Snapxam Calculators Topics Go Premium
ENGESP
Go!
1
2
3
4
5
6
7
8
9
0
x
y
(◻)
◻/◻
2

e
π
ln
log
lim
d/dx
d/dx
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

\int\frac{x-2}{x\cdot\left(x^2+5x-14\right)}dx

Integral of (x-2)/(x(5x-14+x^2))

Answer

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

Step-by-step explanation

Problem

$\int\frac{x-2}{x\cdot\left(x^2+5x-14\right)}dx$
1

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

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

Unlock this step-by-step solution!

Answer

$\frac{1}{7}\ln\left|x\right|-\frac{1}{7}\ln\left|7+x\right|+C_0$
$\int\frac{x-2}{x\cdot\left(x^2+5x-14\right)}dx$

Main topic:

Integrals by partial fraction expansion

Used formulas:

5. See formulas

Time to solve it:

~ 0.39 seconds