Calculators AI Whiteboard Worksheets & Tests
Book solutions
Algebra Baldor
Go Premium Topics

$\int\frac{6x}{x^3-8}dx$

Step-by-step Solution

Go!
Symbolic 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
D□x
∫
∫◻
|◻|
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

Solution

Final answer to the problem

$\ln\left|x-2\right|+3\cdot \left(\frac{1}{\sqrt{3}}\right)\arctan\left(\frac{x+1}{\sqrt{3}}\right)+\ln\left|\frac{\sqrt{3}}{\sqrt{\left(x+1\right)^2+3}}\right|+C_0$
Got another answer? Verify it here!

Step-by-step Solution

How should I solve this problem?

  • Scegliere un'opzione
  • Sostituzione di Weierstrass
  • Prodotto di binomi con termine comune
  • Load more...
Can't find a method? Tell us so we can add it.
1

Rewrite the expression $\frac{6x}{x^3-8}$ inside the integral in factored form

$\int\frac{6x}{\left(x-2\right)\left(x^2+2x+4\right)}dx$

Learn how to solve problems step by step online.

$\int\frac{6x}{\left(x-2\right)\left(x^2+2x+4\right)}dx$

With a free account, access a part of this solution

Unlock the first 3 steps of this solution

Learn how to solve problems step by step online. int((6x)/(x^3-8))dx. Rewrite the expression \frac{6x}{x^3-8} inside the integral in factored form. Apply the formula: \int\frac{ab}{c}dx=a\int\frac{b}{c}dx, where a=6, b=x and c=\left(x-2\right)\left(x^2+2x+4\right). Rewrite the fraction \frac{x}{\left(x-2\right)\left(x^2+2x+4\right)} in 2 simpler fractions using partial fraction decomposition. Expand the integral \int\left(\frac{1}{6\left(x-2\right)}+\frac{-\frac{1}{6}x+\frac{1}{3}}{x^2+2x+4}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately.

Final answer to the problem

$\ln\left|x-2\right|+3\cdot \left(\frac{1}{\sqrt{3}}\right)\arctan\left(\frac{x+1}{\sqrt{3}}\right)+\ln\left|\frac{\sqrt{3}}{\sqrt{\left(x+1\right)^2+3}}\right|+C_0$

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

Help us improve with your feedback!

Function Plot

Plotting: $\ln\left(x-2\right)+3\cdot \left(\frac{1}{\sqrt{3}}\right)\arctan\left(\frac{x+1}{\sqrt{3}}\right)+\ln\left(\frac{\sqrt{3}}{\sqrt{\left(x+1\right)^2+3}}\right)+C_0$

SnapXam A2
Answer Assistant

beta
Got a different answer? Verify it!

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
D□x
∫
∫◻
|◻|
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:

Supercharge your math learning

By signing up, you agree to SnapXam's Terms and Privacy Policy.

Already have an account? Login here
Forgot your password?

Supercharge your math learning



Register here if you don't have an account.
Forgot your password?

Your Personal Math Tutor. Powered by AI

Available 24/7, 365.

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

Includes multiple solving methods.

Download complete solutions and keep them forever.

Premium access on our iOS and Android apps.

Join 500k+ students in problem solving.

Choose your plan. Cancel Anytime.
Pay $39.97 USD securely with your payment method.
Please hold while your payment is being processed.
Create an Account