∫ 1 64 1 + x 3 x d x {\displaystyle \int _{1}^{64}{\frac {1+{\sqrt[{3}]{x}}}{\sqrt {x}}}dx}
∫ 1 64 1 x 1 / 2 {\displaystyle \int _{1}^{64}{\frac {1}{x^{1/2}}}} + ∫ 1 64 x 1 / 3 x 1 / 2 {\displaystyle \int _{1}^{64}{\frac {x^{1/3}}{x^{1/2}}}}
∫ 1 64 x − 1 / 2 + x 1 / 3 − 1 / 2 {\displaystyle \int _{1}^{64}x^{-1/2}+x^{1/3-1/2}} = ∫ 1 64 x − 1 / 2 + x − 1 / 6 {\displaystyle \int _{1}^{64}x^{-1/2}+x^{-1/6}}
Add one to the exponents and divide by the new exponent
∫ 1 64 x 1 / 2 1 2 + x 5 / 6 5 6 {\displaystyle \int _{1}^{64}{\frac {x^{1/2}}{\frac {1}{2}}}+{\frac {x^{5/6}}{\frac {5}{6}}}} = ∫ 1 64 2 x 1 2 + 6 5 x 5 6 {\displaystyle \int _{1}^{64}2x^{\frac {1}{2}}+{\frac {6}{5}}x^{\frac {5}{6}}}
2 ( 64 ) 1 2 + 6 5 ( 64 ) 5 6 − ( 2 ( 1 ) 1 2 + 6 5 ( 1 ) 5 6 ) {\displaystyle 2(64)^{\frac {1}{2}}+{\frac {6}{5}}(64)^{\frac {5}{6}}-(2(1)^{\frac {1}{2}}+{\frac {6}{5}}(1)^{\frac {5}{6}})}
16 + 38.4 − ( 2 + 1.2 ) {\displaystyle 16+38.4-(2+1.2)}
54.4 − 3.2 {\displaystyle 54.4-3.2}
![{\displaystyle \int _{1}^{64}{\frac {1+{\sqrt[{3}]{x}}}{\sqrt {x}}}dx}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/cdb02981593f318bab17caae838949d55b200cb6)
+ 
= 
= 
