What is expand (2(20u^{7/2}-28u^{5/2}))/(35e^x)+C ?

The solution to expand (2(20u^{7/2}-28u^{5/2}))/(35e^x)+C is (8u^{7/2})/(7e^x)-(8u^{5/2})/(5e^x)+C

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expand (2(20u^{7/2}-28u^{5/2}))/(35e^x)+C

expand

\frac{2 ( 20 u ^{\frac{7}{2}} - 28 u ^{\frac{5}{2}} )}{35 e ^{x}} + C

\frac{8 u ^{\frac{7}{2}}}{7 e ^{x}} - \frac{8 u ^{\frac{5}{2}}}{5 e ^{x}} + C

Solution steps

\frac{2 ( 20 u ^{\frac{7}{2}} - 28 u ^{\frac{5}{2}} )}{35 e ^{x}} + C

Expand

2 (20 u^{\frac{7}{2}} - 28 u^{\frac{5}{2}}) : 40 u^{\frac{7}{2}} - 56 u^{\frac{5}{2}}

= \frac{40 u ^{\frac{7}{2}} - 56 u ^{\frac{5}{2}}}{35 e ^{x}} + C

Apply the fraction rule:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{40 u ^{\frac{7}{2}} - 56 u ^{\frac{5}{2}}}{35 e ^{x}} = \frac{40 u ^{\frac{7}{2}}}{35 e ^{x}} - \frac{56 u ^{\frac{5}{2}}}{35 e ^{x}}

= \frac{40 u ^{\frac{7}{2}}}{35 e ^{x}} - \frac{56 u ^{\frac{5}{2}}}{35 e ^{x}} + C

Cancel

\frac{40 u ^{\frac{7}{2}}}{35 e ^{x}} : \frac{8 u ^{\frac{7}{2}}}{7 e ^{x}}

= \frac{8 u ^{\frac{7}{2}}}{7 e ^{x}} - \frac{56 u ^{\frac{5}{2}}}{35 e ^{x}} + C

Cancel

\frac{56 u ^{\frac{5}{2}}}{35 e ^{x}} : \frac{8 u ^{\frac{5}{2}}}{5 e ^{x}}

= \frac{8 u ^{\frac{7}{2}}}{7 e ^{x}} - \frac{8 u ^{\frac{5}{2}}}{5 e ^{x}} + C

\frac{2 x ^{2} - 1}{x ( x ^{2} - 1 )}

(csc (a) + 1) (sec (a) - tan (a))

- \frac{5 ( - 2 y + x )}{4}

\frac{2 ( 5 + s ^{2} )}{( s - 2 ) ( s + 2 ) ( s ^{2} + 4 )}

0.2707065 (\frac{1}{π} arctan (\frac{0.15}{x}) + 0.5)

What is expand (2(20u^{7/2}-28u^{5/2}))/(35e^x)+C ?
The solution to expand (2(20u^{7/2}-28u^{5/2}))/(35e^x)+C is (8u^{7/2})/(7e^x)-(8u^{5/2})/(5e^x)+C