Final answer to the problem
$-3fx+5xf\ln\left|x\right|+\frac{f}{\sqrt{3}}\ln\left|\sqrt{3}x+\sqrt{3}-1\right|+\frac{-f}{\sqrt{3}}\ln\left|\sqrt{3}x+\sqrt{3}+1\right|-f\ln\left|-\frac{1}{3}+\left(x+1\right)^2\right|-fx\ln\left|3x^2+6x+2\right|+C_0$
Got another answer? Verify it here!
Step-by-step Solution
How should I solve this problem?
- Integrate using trigonometric identities
- Integrate by partial fractions
- Integrate by substitution
- Integrate by parts
- Integrate using tabular integration
- Integrate by trigonometric substitution
- Weierstrass Substitution
- Integrate using basic integrals
- Product of Binomials with Common Term
- FOIL Method
- Load more...
Can't find a method? Tell us so we can add it.
1
Find the integral
$\int f\ln\left(\frac{x^5}{3x^2+6x+2}\right)dx$
Learn how to solve differential calculus problems step by step online.
$\int f\ln\left(\frac{x^5}{3x^2+6x+2}\right)dx$
Learn how to solve differential calculus 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
$-3fx+5xf\ln\left|x\right|+\frac{f}{\sqrt{3}}\ln\left|\sqrt{3}x+\sqrt{3}-1\right|+\frac{-f}{\sqrt{3}}\ln\left|\sqrt{3}x+\sqrt{3}+1\right|-f\ln\left|-\frac{1}{3}+\left(x+1\right)^2\right|-fx\ln\left|3x^2+6x+2\right|+C_0$
