What is the integral of 2sin(x)-2x^{5/2}+C ?

The integral of 2sin(x)-2x^{5/2}+C is -2cos(x)-4/7 x^{7/2}+Cx+C

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integral of 2sin(x)-2x^{5/2}+C

\int 2 sin (x) - 2 x^{\frac{5}{2}} + C d x

- 2 cos (x) - \frac{4}{7} x^{\frac{7}{2}} + C x + C

Solution steps

\int 2 sin (x) - 2 x^{\frac{5}{2}} + C d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 2 sin (x) d x - \int 2 x^{\frac{5}{2}} d x + \int C d x

\int 2 sin (x) d x = - 2 cos (x)

\int 2 x^{\frac{5}{2}} d x = \frac{4}{7} x^{\frac{7}{2}}

\int C d x = C x

= - 2 cos (x) - \frac{4}{7} x^{\frac{7}{2}} + C x

Add a constant to the solution

= - 2 cos (x) - \frac{4}{7} x^{\frac{7}{2}} + C x + C

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\int \frac{2 x + 1}{( 2 x ^{2} + 2 x ) ^{2}} d x

What is the integral of 2sin(x)-2x^{5/2}+C ?
The integral of 2sin(x)-2x^{5/2}+C is -2cos(x)-4/7 x^{7/2}+Cx+C