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

x \to 3 + lim (\frac{1}{x + 3})

(x + e^{y}) y^{^{'}} = x e^{- y} - 1

2^{x - 1}

x \frac{d y}{d x} + 5 y = x^{3} - x

7 e^{x}, 7 x e^{x^{2}}, 0, 1

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