Final answer to the problem
$\ln\left|2\right|x+x-x\ln\left|x\right|+C_0$
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Step-by-step Solution
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- 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
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1
The logarithm of a quotient is equal to the logarithm of the numerator minus the logarithm of the denominator
$\int\left(\ln\left(2\right)-\ln\left(x\right)\right)dx$
Learn how to solve differential calculus problems step by step online. Solve the integral of logarithmic functions int(ln(2/x))dx. 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(2\right)-\ln\left(x\right)\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int\ln\left(2\right)dx results in: \ln\left(2\right)x. Multiply the single term -1 by each term of the polynomial \left(x\ln\left(x\right)-x\right).
Final answer to the problem
$\ln\left|2\right|x+x-x\ln\left|x\right|+C_0$
