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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

Answers (1)

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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