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Question Number 54995 by peter frank last updated on 15/Feb/19

$$\int \sqrt[3]{x^3+x^2}dx$$

Commented by MJS last updated on 16/Feb/19

$$\mathrm{I}\mathrm{can}\mathrm{solve}\mathrm{this}\mathrm{but}{\mathrm{it}}^{\prime }\mathrm{s}\mathrm{a}\mathrm{lot}\mathrm{of}\mathrm{typing}\mathrm{work}$$$$\mathrm{if}\mathrm{you}\mathrm{need}\mathrm{it}\mathrm{urgently}\mathrm{I}\mathrm{will}\mathrm{post}\mathrm{it}$$

Commented by peter frank last updated on 16/Feb/19

$$pleasesirpostit....itwill$$$$helpfultomeandothers$$$$$$

Commented by MJS last updated on 16/Feb/19

$$\mathrm{ok}\mathrm{might}\mathrm{take}\mathrm{some}\mathrm{time}$$

Answered by tanmay.chaudhury50@gmail.com last updated on 16/Feb/19

$$\int x^{\frac{2}{3}}{(1+x)}^{\frac{1}{3}}dx$$$$\int x^{\frac{2}{3}}[1+\frac{1}{3}x+\frac{1}{3}(\frac{1}{3}-1)\frac{x^2}{2!}+\frac{1}{3}(\frac{1}{3}-1)(\frac{1}{3}-2)\frac{x^3}{3!}+...]dx$$$$\int x^{\frac{2}{3}}+\frac{1}{3}{x}^{\frac{5}{3}}+\frac{1}{3}(\frac{1}{3}-1)x^{\frac{8}{3}}\times \frac{1}{2!}+\frac{1}{3}(\frac{1}{3}-1)(\frac{1}{3}-2)\frac{x^{\frac{11}{3}}}{3!}+...]dx$$$$sointheformof...$$$$\int x^{\frac{2}{3}}+a_1{x}^{\frac{5}{3}}+a_2{x}^{\frac{8}{3}}+a_3{x}^{\frac{11}{3}}+...dx$$$$\frac{x^{\frac{5}{3}}}{\frac{5}{3}}+a_1\times \frac{x^{\frac{8}{3}}}{\frac{8}{3}}+a_2\frac{x^{\frac{11}{3}}}{\frac{11}{3}}+....$$

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