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Question Number 123703 by Algoritm last updated on 27/Nov/20

Answered by MJS_new last updated on 27/Nov/20

$$=\int {\left(\cos x\right)}^{5/3}dx$$$$\mathrm{use}\mathrm{these}\mathrm{formulas}:$$$$\int {\left(\sin x\right)}^{p/q}dx=\frac{q}{p+q}{\left(\sin x\right)}^{\frac{p+q}{q}}{}_2{\mathrm{F}}_1(\frac{1}{2},\frac{p+q}{2q};\frac{p+3q}{2q};{\sin }^{2}x)+C$$$$\int {\left(\cos x\right)}^{p/q}dx=-\frac{q}{p+q}{\left(\cos x\right)}^{\frac{p+q}{q}}{}_2{\mathrm{F}}_1(\frac{1}{2},\frac{p+q}{2q};\frac{p+3q}{2q};{\cos }^{2}x)+C$$$$$$

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