Final answer to the problem
Step-by-step Solution
How should I solve this problem?
- Integrate by partial fractions
- Integrate by substitution
- Integrate by parts
- Integrate using tabular integration
- Integrate by trigonometric substitution
- Weierstrass Substitution
- Integrate using trigonometric identities
- Integrate using basic integrals
- Product of Binomials with Common Term
- FOIL Method
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Rewrite the expression $\frac{x-2}{x\left(x^2+5x-14\right)}$ inside the integral in factored form
Learn how to solve integrals by partial fraction expansion problems step by step online.
$\int\frac{1}{x\left(x+7\right)}dx$
Learn how to solve integrals by partial fraction expansion problems step by step online. Find the integral int((x-2)/(x(x^2+5x+-14)))dx. Rewrite the expression \frac{x-2}{x\left(x^2+5x-14\right)} inside the integral in factored form. Rewrite the fraction \frac{1}{x\left(x+7\right)} in 2 simpler fractions using partial fraction decomposition. Expand the integral \int\left(\frac{1}{7x}+\frac{-1}{7\left(x+7\right)}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. We can solve the integral \int\frac{-1}{7\left(x+7\right)}dx by applying integration by substitution method (also called U-Substitution). First, we must identify a section within the integral with a new variable (let's call it u), which when substituted makes the integral easier. We see that x+7 it's a good candidate for substitution. Let's define a variable u and assign it to the choosen part.