Value of {x²}{x+2} dx is

Correct Answer is : 2xlog⁡(x+2)+c2x (x+2) + c2xlog(x+2)+c

Correct Answer is : 2xlog⁡(x+2)+c2x (x+2) + c2xlog(x+2)+c

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Integral Calculus

Question : 8 of 73

Marks: +1, -0

Value of

\int \frac{x^{2}}{x+2} dx

Solution:

Concept:

Use polynomial division to simplify the integrand, then integrate term by term.

Explanation:

<br>\frac{x^2}{x+2} = x - 2 + \frac{4}{x+2}<br>

using long division.

Now integrate:

<br>\int \frac{x^2}{x+2}dx = \int (x - 2 + \frac{4}{x+2})dx = \frac{x^2}{2} - 2x + 4\ln|x+2| + c<br>

Note:

\log

denotes natural logarithm as per the options.

Answer:

\frac{x^{2}}{2} - 2x + 4 \log (x+2) + c

, which corresponds to option B.

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