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Question Number 152502 by Tawa11 last updated on 29/Aug/21

$$\int {9\mathrm{x}}^2{({4\mathrm{x}}^2+3)}^{10}\mathrm{dx}$$

Answered by Olaf_Thorendsen last updated on 30/Aug/21

$$\mathrm{F}\left(x\right)=\int 9x^2{(4x^2+3)}^{10}dx$$$$\mathrm{F}\left(x\right)=3^{12}\int \underset{k=0}{\sum ^{10}}{\mathrm{C}}_k^{10}{\left(\frac{4}{3}\right)}^k{x}^{2k+2}dx$$$$\mathrm{F}\left(x\right)=3^{12}\underset{k=0}{\sum ^{10}}{\mathrm{C}}_k^{10}{\left(\frac{4}{3}\right)}^k\frac{x^{2k+3}}{2k+3}+\mathrm{C}$$

Commented by Tawa11 last updated on 30/Aug/21

$$\mathrm{God}\mathrm{bless}\mathrm{you}\mathrm{sir}.$$

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