Try NerdPal! Our new app on iOS and Android

Integrate the function $\frac{1}{x^2-6x+5}$ from $2$ to $4$

Step-by-step Solution

Go!
Go!
1
2
3
4
5
6
7
8
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
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

Final Answer

The integral diverges.

Step-by-step Solution

Problem to solve:

$\int_{2}^{4}\frac{1}{x^2-6x+5}dx$

Specify the solving method

1

Rewrite the expression $\frac{1}{x^2-6x+5}$ inside the integral in factored form

$\int_{2}^{4}\frac{1}{\left(x-1\right)\left(x-5\right)}dx$
2

Rewrite the fraction $\frac{1}{\left(x-1\right)\left(x-5\right)}$ in $2$ simpler fractions using partial fraction decomposition

$\frac{1}{\left(x-1\right)\left(x-5\right)}=\frac{A}{x-1}+\frac{B}{x-5}$

Learn how to solve definite integrals problems step by step online.

$\int_{2}^{4}\frac{1}{\left(x-1\right)\left(x-5\right)}dx$

Unlock this complete solution and much more!

As low as $3.97 USD / week. Cancel anytime.

Learn how to solve definite integrals problems step by step online. Integrate the function 1/(x^2-6x+5) from 2 to 4. Rewrite the expression \frac{1}{x^2-6x+5} inside the integral in factored form. Rewrite the fraction \frac{1}{\left(x-1\right)\left(x-5\right)} in 2 simpler fractions using partial fraction decomposition. Find the values for the unknown coefficients: A, B. The first step is to multiply both sides of the equation from the previous step by \left(x-1\right)\left(x-5\right). Multiplying polynomials.

Final Answer

The integral diverges.

Explore different ways to solve this problem

Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

Solve int(1/(x^2-6x+5))dx&2&4 using partial fractionsSolve int(1/(x^2-6x+5))dx&2&4 using basic integralsSolve int(1/(x^2-6x+5))dx&2&4 using u-substitutionSolve int(1/(x^2-6x+5))dx&2&4 using integration by partsSolve int(1/(x^2-6x+5))dx&2&4 using trigonometric substitution
$\int_{2}^{4}\frac{1}{x^2-6x+5}dx$

Main topic:

Definite Integrals

Used formulas:

3. See formulas

Time to solve it:

~ 0.12 s