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  • Please solve rd sharma class 12 chapter Indefinite integrals exercise 18.4 question 2 maths textbook solution

Please solve rd sharma class 12 chapter Indefinite integrals exercise 18.4 question 2 maths textbook solution

Answers (1)

best_answer

Answer:

\Rightarrow \frac{x^{3}}{3}+x^{2}+4x-8\log \left | x-2 \right |+C

Hint:

Divide denominator by numerator.

Given:

\Rightarrow \int \frac{x^{3}}{x-2}dx

Solution:

\Rightarrow \int \frac{x^{3}}{x-2}dx

\Rightarrow \int \left ( x^{2}+2x+4 \right )dx+\frac{8}{\int \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 x^{2}dx+2\int xdx+4\int dx+8\int \frac{dx}{\left ( x-2 \right )}

\Rightarrow \frac{x^{3}}{3}+x^{2}+4x-8\log \left | x-2 \right |+C

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