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  • please solve rd sharma class 12 chapter Indefinite Integrals exercise 18.2 question 2 maths textbook solution

please solve rd sharma class 12 chapter Indefinite Integrals exercise 18.2 question 2 maths textbook solution

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\frac{2^{x}}{\log 2}+5 \log x-\frac{3}{2} x^{\frac{2}{3}}+c

Hint: To solve this equation we differentiate it differently.

\begin{aligned} &\text { Given: } \int\left(2^{x}+\frac{5}{x}-\frac{1}{x^{\frac{1}{3}}}\right) d x \\ &\text { Solution: } \int 2^{x} d x+5 \int \frac{1}{x} d x-\int \frac{1}{x^{\frac{1}{3}}} d x \\ &\left\{\begin{array}{l} \int a^{x} d x=\frac{a^{x}}{\log a}+c \\ \int \frac{1}{x} d x=\log x+c \end{array}\right\} \\ &=\frac{2^{x}}{\log 2}+5 \log x-\frac{x^{-\frac{3}{2}+1}}{-\frac{3}{2}+1}+c \\ &=\frac{2^{x}}{\log 2}+5 \log x-\frac{3}{2} x^{\frac{2}{3}}+c \end{aligned}

 

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