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f(x)=(x-6)/(x+2)−6−5−4−3−2−10123456−3-2.5−2-1.5−1-0.500.511.522.53xy

Exercise

∫x−6x+2dx\int\frac{x-6}{x+2}dx

Step-by-step Solution

Learn how to solve trigonometric equations problems step by step online. Find the integral int((x-6)/(x+2))dx. Expand the fraction \frac{x-6}{x+2} into 2 simpler fractions with common denominator x+2. Expand the integral \int\left(\frac{x}{x+2}+\frac{-6}{x+2}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int\frac{x}{x+2}dx results in: x+2-2\ln\left(x+2\right). Gather the results of all integrals.
Find the integral int((x-6)/(x+2))dx

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Final answer to the exercise

−8ln⁡∣x+2∣+x+C1-8\ln\left|x+2\right|+x+C_1

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  • Integrate by partial fractions
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∫x−6x+2 dx
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