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provide solution for RD Sharma maths class 12 chapter indefinite integrals exercise 18.4 question 1

Answers (1)

Answer:

\frac{x^{2}}{2}+3x-4\log \left | x+2 \right |+C

Hint:

Divide numerator by denominator.

Given:

\int \frac{x^{2}+5x+2}{x+2}

Solution:

\int \frac{x^{2}+5x+2}{x+2}

\Rightarrow \int \left ( x+3 \right )dx-4\int \frac{1}{\left ( x+2 \right )}dx                                \left [ \int x^{n}dx=\frac{x^{n+1}}{n+1}+C \right ]  &  \left [ \int \frac{1}{x}dx=\log \left | x \right |+C \right ]

\Rightarrow \int xdx+3\int dx-4\int \frac{1}{\left ( x+2 \right )}dx

\Rightarrow \frac{x^{2}}{2}+3x-4\log \left | x+2 \right |+C

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