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  • Provide solution for rd sharma maths class 12 chapter Indefinite Integrals exercise 18.2 question 18

Provide solution for rd sharma maths class 12 chapter Indefinite Integrals exercise 18.2 question 18

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3 x^{3}+12 x^{2}+16 x+c

Hint: To solve this equation we do middle term equation

\begin{aligned} &\text { Given: } \int(3 x+4)^{2} d x \\ &\text { Solution: }(3 x+4)^{2} \\ &=(3 x)^{2}+(4)^{2}+2(3 x)(4) \\ &=9 x^{2}+16+24 x \\ &=9 x^{2}+24 x+16 \\ &=\int (3 x+4)^{2} d x=\int 9 x^{2}+24 x+16 d x \\ &=9 \frac{1}{1+2} x^{1+2}+24 \frac{1}{1+1} x^{1+1}+16 x+c \quad\left[\int x^{a} d x=\frac{1}{a} x^{a+1}+c, a \neq-1\right] \\ &=\frac{9}{3} x^{3}+\frac{24}{2} x^{2}+16 x+c \end{aligned}

3 x^{3}+12 x^{2}+16 x+c

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