What is the integral of sqrt(x)-9cos(x) ?

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

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integral of sqrt(x)-9cos(x)

\int x - 9 cos (x) d x

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

Solution steps

\int x - 9 cos (x) 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 x d x - \int 9 cos (x) d x

\int x d x = \frac{2}{3} x^{\frac{3}{2}}

\int 9 cos (x) d x = 9 sin (x)

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

Add a constant to the solution

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

y = \frac{5}{x}, y = \frac{5}{x ^{2}}, x = 6

x \to 0 lim (x^{x^{x}})

(x^{2} + 1) \frac{d y}{d x} + x y - x = 0

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

n = 0 \sum \infty 3 (x - 2)^{n}

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