What is the integral of 2/3 x^{3/2}-4sin(x)+C ?

The integral of 2/3 x^{3/2}-4sin(x)+C is 4/15 x^{5/2}+4cos(x)+Cx+C

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integral of 2/3 x^{3/2}-4sin(x)+C

\int \frac{2}{3} x^{\frac{3}{2}} - 4 sin (x) + C d x

\frac{4}{15} x^{\frac{5}{2}} + 4 cos (x) + C x + C

Solution steps

\int \frac{2}{3} x^{\frac{3}{2}} - 4 sin (x) + 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 \frac{2}{3} x^{\frac{3}{2}} d x - \int 4 sin (x) d x + \int C d x

\int \frac{2}{3} x^{\frac{3}{2}} d x = \frac{4}{15} x^{\frac{5}{2}}

\int 4 sin (x) d x = - 4 cos (x)

\int C d x = C x

= \frac{4}{15} x^{\frac{5}{2}} - (- 4 cos (x)) + C x

Simplify

= \frac{4}{15} x^{\frac{5}{2}} + 4 cos (x) + C x

Add a constant to the solution

= \frac{4}{15} x^{\frac{5}{2}} + 4 cos (x) + C x + C

\frac{d}{d x} ((2 x - 1)^{3})

\frac{1}{cos ( t )}

f (x) = \frac{1}{5 x}, at x = 9

\frac{36}{9 + x ^{2}}, 1

\frac{d}{d x} (3 x - 2 y)

What is the integral of 2/3 x^{3/2}-4sin(x)+C ?
The integral of 2/3 x^{3/2}-4sin(x)+C is 4/15 x^{5/2}+4cos(x)+Cx+C