What is the integral of 2/3 x^{3/2}-9sin(x)+C ?

The integral of 2/3 x^{3/2}-9sin(x)+C is 4/15 x^{5/2}+9cos(x)+Cx+C

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integral of 2/3 x^{3/2}-9sin(x)+C

\int \frac{2}{3} x^{\frac{3}{2}} - 9 sin (x) + C d x

\frac{4}{15} x^{\frac{5}{2}} + 9 cos (x) + C x + C

Solution steps

\int \frac{2}{3} x^{\frac{3}{2}} - 9 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 9 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 9 sin (x) d x = - 9 cos (x)

\int C d x = C x

= \frac{4}{15} x^{\frac{5}{2}} - (- 9 cos (x)) + C x

Simplify

= \frac{4}{15} x^{\frac{5}{2}} + 9 cos (x) + C x

Add a constant to the solution

= \frac{4}{15} x^{\frac{5}{2}} + 9 cos (x) + C x + C

x \to 1 + lim (ln (x^{2} - 1))

\int x (x - 1) d x

\frac{d ^{2}}{d x ^{2}} ((x^{2} + 6)^{7})

g (x) = sin (x), 0, \frac{π}{4}

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

What is the integral of 2/3 x^{3/2}-9sin(x)+C ?
The integral of 2/3 x^{3/2}-9sin(x)+C is 4/15 x^{5/2}+9cos(x)+Cx+C