👉 Try now NerdPal! Our new math app on iOS and Android

Integrate the function $\frac{8x}{x^2-4}$ from $2$ to $4$

Step-by-step Solution

Go!
Math mode
Text mode
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

Specify the solving method

1

Rewrite the expression $\frac{8x}{x^2-4}$ inside the integral in factored form

$\int_{2}^{4}\frac{8x}{\left(x+2\right)\left(x-2\right)}dx$

Learn how to solve differential calculus problems step by step online.

$\int_{2}^{4}\frac{8x}{\left(x+2\right)\left(x-2\right)}dx$

Unlock unlimited step-by-step solutions and much more!

Unlock the first 2 steps of this solution.

Learn how to solve differential calculus problems step by step online. Integrate the function (8x)/(x^2-4) from 2 to 4. Rewrite the expression \frac{8x}{x^2-4} inside the integral in factored form. Take out the constant 8 from the integral. Rewrite the fraction \frac{x}{\left(x+2\right)\left(x-2\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+2\right)\left(x-2\right).

Final Answer

The integral diverges.

Explore different ways to solve this problem

Give us your feedback!

Function Plot

Plotting: $\frac{8x}{x^2-4}$

Main Topic: Differential Calculus

The derivative of a function of a real variable measures the sensitivity to change of a quantity (a function value or dependent variable) which is determined by another quantity (the independent variable). Derivatives are a fundamental tool of calculus.

Used Formulas

1. See formulas

Your Math & Physics Tutor. Powered by AI

Available 24/7, 365.

Complete step-by-step math solutions. No ads.

Includes multiple solving methods.

Support for more than 100 math topics.

Premium access on our iOS and Android apps as well.

20% discount on online tutoring.

Choose your Subscription plan:
Have a promo code?
Pay $39.97 USD securely with your payment method.
Please hold while your payment is being processed.
Create an Account