What is the integral of 2/3 x^{3/2}-6sin(x)+C ?

The integral of 2/3 x^{3/2}-6sin(x)+C is 4/15 x^{5/2}+6cos(x)+Cx+C

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integral of 2/3 x^{3/2}-6sin(x)+C

\int \frac{2}{3} x^{\frac{3}{2}} - 6 sin (x) + C d x

\frac{4}{15} x^{\frac{5}{2}} + 6 cos (x) + C x + C

Solution steps

\int \frac{2}{3} x^{\frac{3}{2}} - 6 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 6 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 6 sin (x) d x = - 6 cos (x)

\int C d x = C x

= \frac{4}{15} x^{\frac{5}{2}} - (- 6 cos (x)) + C x

Simplify

= \frac{4}{15} x^{\frac{5}{2}} + 6 cos (x) + C x

Add a constant to the solution

= \frac{4}{15} x^{\frac{5}{2}} + 6 cos (x) + C x + C

y^{^{'}} = x^{2} - 1, y (0) = 1

\int \frac{1}{289 + x ^{2}} d x

\int_{0}^{1} (x^{15} + 1 5^{x}) d x

x^{2} y^{^{''}} - x y^{^{'}} + y = x

x \to 9 - lim (x^{2} - 3 x)

What is the integral of 2/3 x^{3/2}-6sin(x)+C ?
The integral of 2/3 x^{3/2}-6sin(x)+C is 4/15 x^{5/2}+6cos(x)+Cx+C