Final answer to the problem
$-3fx+5xf\ln\left|x\right|-f\ln\left|v\right|+\frac{2wf}{\sqrt{3}\left(-1+w^2\right)}-fx\ln\left|3x^2+6x+2\right|+C_0$
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Step-by-step Solution
How should I solve this problem?
- Integrate using tabular integration
- Integrate by partial fractions
- Integrate by substitution
- Integrate by parts
- 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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1
Find the integral
$\int f\ln\left(\frac{x^5}{3x^2+6x+2}\right)dx$
Learn how to solve problems step by step online.
$\int f\ln\left(\frac{x^5}{3x^2+6x+2}\right)dx$
Learn how to solve problems step by step online. Integrate the function fln((x^5)/(3x^2+6x+2)). Find the integral. The integral of a function times a constant (f) is equal to the constant times the integral of the function. The logarithm of a quotient is equal to the logarithm of the numerator minus the logarithm of the denominator. Expand the integral \int\left(\ln\left(x^5\right)-\ln\left(3x^2+6x+2\right)\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately.
Final answer to the problem
$-3fx+5xf\ln\left|x\right|-f\ln\left|v\right|+\frac{2wf}{\sqrt{3}\left(-1+w^2\right)}-fx\ln\left|3x^2+6x+2\right|+C_0$
