Math virtual assistant

Calculators Topics Go Premium About Snapxam
ENGESP

Step-by-step Solution

Integral of (1-3x)/(x^2+2x-8)

Go
1
2
3
4
5
6
7
8
9
0
x
y
(◻)
◻/◻
2

e
π
ln
log
lim
d/dx
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

Answer

$-\frac{5}{6}\ln\left|x-2\right|-\frac{13}{6}\ln\left|x+4\right|+C_0$

Step-by-step explanation

Problem to solve:

$\int\frac{1-3x}{x^2+2x-8}dx$
1

Factor the trinomial $x^2+2x-8$ finding two numbers that multiply to form $-8$ and added form $2$

$\begin{matrix}\left(-2\right)\left(4\right)=-8\\ \left(-2\right)+\left(4\right)=2\end{matrix}$
2

Thus

$\int\frac{1-3x}{\left(x-2\right)\left(x+4\right)}dx$

Unlock this step-by-step solution!

Answer

$-\frac{5}{6}\ln\left|x-2\right|-\frac{13}{6}\ln\left|x+4\right|+C_0$

Struggling with math?

Access detailed step by step solutions to millions of problems, growing every day!