Answer to Question #136199 in Calculus for qwerty

Question #136199
\int \:\left(x^{\frac{2}{3}}-\frac{1}{x^{\frac{2}{3}}}+\frac{2}{x^5}-2x\right)dx
1
Expert's answer
2020-10-01T17:18:39-0400

(x231x23+2x52x)dx=x23dxx23dx+2x5dx2x1dx=\int \left(x^{\frac{2}{3}}-\frac{1}{x^{\frac{2}{3}}}+\frac{2}{x^5}-2x\right)dx=\int x^{\frac{2}{3}}dx-\int x^{-\frac{2}{3}}dx+2\int x^{-5}dx-2\int x^1dx=

=x23+123+1x23+123+1+2x5+15+12x1+11+1+C==\frac{x^{{\frac{2}{3}}+1}}{\frac{2}{3}+1} -\frac{x^{-{\frac{2}{3}}+1}}{-\frac{2}{3}+1} +2\frac{x^{-5+1}}{-5+1} -2\frac{x^{1+1}}{1+1}+C=

=3x5353x13+2x442x22+C==\frac{3x^{\frac{5}{3}}}{5}-3x^{\frac{1}{3}}+2\frac{x^{-4}}{-4}-2\frac{x^2}{2}+C=

=35x533x312x4x2+C=\frac{3}{5}{x^{\frac{5}{3}}}-3\sqrt[3]{x}-\frac{1}{2x^4}-x^2+C.

Answer: 35x533x312x4x2+C\frac{3}{5}{x^{\frac{5}{3}}}-3\sqrt[3]{x}-\frac{1}{2x^4}-x^2+C.


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