Final answer to the problem
Step-by-step Solution
How should I solve this problem?
- Integrate by substitution
- Integrate by partial fractions
- 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 fraction $\frac{7x^2+2x-3}{\left(2x-1\right)\left(3x+2\right)\left(x-3\right)}$ in $3$ simpler fractions using partial fraction decomposition
Learn how to solve integrals by partial fraction expansion problems step by step online.
$\frac{1}{35\left(2x-1\right)}+\frac{-1}{7\left(3x+2\right)}+\frac{6}{5\left(x-3\right)}$
Learn how to solve integrals by partial fraction expansion problems step by step online. Find the integral int((7x^2+2x+-3)/((2x-1)(3x+2)(x-3)))dx. Rewrite the fraction \frac{7x^2+2x-3}{\left(2x-1\right)\left(3x+2\right)\left(x-3\right)} in 3 simpler fractions using partial fraction decomposition. Expand the integral \int\left(\frac{1}{35\left(2x-1\right)}+\frac{-1}{7\left(3x+2\right)}+\frac{6}{5\left(x-3\right)}\right)dx into 3 integrals using the sum rule for integrals, to then solve each integral separately. We can solve the integral \int\frac{1}{35\left(2x-1\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 2x-1 it's a good candidate for substitution. Let's define a variable u and assign it to the choosen part. Now, in order to rewrite dx in terms of du, we need to find the derivative of u. We need to calculate du, we can do that by deriving the equation above.
