What is the integral of (sqrt(25-x^2)-3) ?

The integral of (sqrt(25-x^2)-3) is 25/2 (arcsin(1/5 x)+1/2 sin(2arcsin(1/5 x)))-3x+C

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integral of (sqrt(25-x^2)-3)

\int (25 - x^{2} - 3) d x

\frac{25}{2} (arcsin (\frac{1}{5} x) + \frac{1}{2} sin (2 arcsin (\frac{1}{5} x))) - 3 x + C

Solution steps

\int 25 - x^{2} - 3 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 25 - x^{2} d x - \int 3 d x

\int 25 - x^{2} d x = \frac{25}{2} (arcsin (\frac{1}{5} x) + \frac{1}{2} sin (2 arcsin (\frac{1}{5} x)))

\int 3 d x = 3 x

= \frac{25}{2} (arcsin (\frac{1}{5} x) + \frac{1}{2} sin (2 arcsin (\frac{1}{5} x))) - 3 x

Add a constant to the solution

= \frac{25}{2} (arcsin (\frac{1}{5} x) + \frac{1}{2} sin (2 arcsin (\frac{1}{5} x))) - 3 x + C

n = 3 \sum \infty (\frac{3}{11})^{- n}

\int \frac{8}{x ln ( 2 x )} d x

\frac{\partial}{\partial x} (e^{- x y})

x \to + 2 + lim (x^{2})

\frac{d}{d x} (z arctan (\frac{y}{x}))

What is the integral of (sqrt(25-x^2)-3) ?
The integral of (sqrt(25-x^2)-3) is 25/2 (arcsin(1/5 x)+1/2 sin(2arcsin(1/5 x)))-3x+C