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Need solution for RD Sharma Maths Class 12 Chapter 18 Indefiite Integrals Excercise Fill in the Blanks Question 11

Answers (1)

Answer:

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

Hint:

Simplify it and integrate it.

Solution:

I=\int \frac{e^{5 \log _{\varepsilon} x}-e^{4 \log _{e} x}}{e^{3 \log _{e} x}-e^{2 \log _{e} x}} d x

I=\int \frac{e^{\log _{e} x^{5}}-e^{\log _{\varepsilon} x^{4}}}{e^{\log _{e} x^{3}}-e^{\log _{\varepsilon} x^{2}}} d x

I=\int \frac{x^{5}-x^{4}}{x^{3}-x^{2}} d x

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

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