👉 Try now NerdPal! Our new math app on iOS and Android
Calculators Topics Solving Methods Step Checker
Book solutions
Algebra Baldor
Go Premium Topics

Integrate the function $\frac{x}{x^3-3x+2}$ from $-\frac{1}{2}$ to $\frac{1}{2}$

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
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

Formulas

Videos

Final Answer

The integral diverges.

Step-by-step Solution

Specify the solving method

1

Rewrite the expression $\frac{x}{x^3-3x+2}$ inside the integral in factored form

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

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

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

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

Create a free account and unlock a glimpse of this solution.

Learn how to solve definite integrals problems step by step online. Integrate the function x/(x^3-3x+2) from -1/2 to 1/2. Rewrite the expression \frac{x}{x^3-3x+2} inside the integral in factored form. Rewrite the fraction \frac{x}{\left(x-1\right)^{2}\left(x+2\right)} in 3 simpler fractions using partial fraction decomposition. Find the values for the unknown coefficients: A, B, C. The first step is to multiply both sides of the equation from the previous step by \left(x-1\right)^{2}\left(x+2\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 integral of (x/(x^3+-3x))dx from -0.5 to 0.5 using partial fractionsSolve integral of (x/(x^3+-3x))dx from -0.5 to 0.5 using basic integralsSolve integral of (x/(x^3+-3x))dx from -0.5 to 0.5 using u-substitutionSolve integral of (x/(x^3+-3x))dx from -0.5 to 0.5 using integration by partsSolve integral of (x/(x^3+-3x))dx from -0.5 to 0.5 using trigonometric substitution

Give us your feedback!

Function Plot

Plotting: $\frac{x}{x^3-3x+2}$

Similar Problems Solved

Evaluate the integral

$\int_0^{\infty}\left(\frac{1}{1+x^2}\right)dx$

Evaluate the integral

$\int_{1}^{3}\cos\left(x\right)^2dx$

Evaluate the integral

$\int_{-5}^{5}\frac{1}{\sqrt{5-x}}dx$

Evaluate the integral

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

Evaluate the integral

$\int_{2}^{4}\left(x^2+5x+6\right)dx$

Evaluate the integral

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

Evaluate the integral

$\int_{1}^{2}\frac{1}{x\cdot\left(x+1\right)}dx$

Main Topic: Definite Integrals

Given a function f(x) and the interval [a,b], the definite integral is equal to the area that is bounded by the graph of f(x), the x-axis and the vertical lines x=a and x=b

Used Formulas

3. See formulas

Related Topics

Supercharge your math learning

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

Already have an account? Login here
Forgot password?

Supercharge your math learning



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

Your Math & Physics Tutor. Powered by AI

Available 24/7, 365.

Unlimited 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