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  • Need solution for RD Sharma Maths Class 12 Chapter 18 Indefiite Integrals Excercise Fill in the Blanks Question 12

Need solution for RD Sharma Maths Class 12 Chapter 18 Indefiite Integrals Excercise Fill in the Blanks Question 12

Answers (1)

Answer:

\frac{x^{3}}{3}+\frac{x^{2}}{2}+x+c

Hint:

Simplify it by factorizing the numerator and then integrate it.

Solution:

\begin{aligned} &I=\int \frac{x^{4}+x^{2}+1}{x^{2}-x+1} d x \\ &I=\int \frac{\left(x^{2}-x+1\right)\left(x^{2}+x+1\right)}{x^{2}-x+1} d x \\ &I=\int\left(x^{2}+x+1\right) d x \\ &I=\frac{x^{3}}{3}+\frac{x^{2}}{2}+x+c \end{aligned}

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