What is the integral of sqrt(x)-4cos(x) ?

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

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integral of sqrt(x)-4cos(x)

\int x - 4 cos (x) d x

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

Solution steps

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

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

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

= \frac{2}{3} x^{\frac{3}{2}} - 4 sin (x)

Add a constant to the solution

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

\int_{0}^{t} t^{2} e^{- 2 t} d t

\int 3 4^{2 x} d x

3 e^{x} - 7, at x = 0

\frac{\partial}{\partial x} (\frac{- 8 x}{x ^{2} + 1})

y = 4 + 5 x^{2} - 2 x^{3}, at x = a

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