What is the integral of (4-x^2)^{1.5} ?

The integral of (4-x^2)^{1.5} is x(4-x^2)^{1.5}+6(arcsin(0.5x)-0.25sin(4arcsin(0.5x)))+C

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integral of (4-x^2)^{1.5}

integral

(4 - x^{2})^{1.5}

x (4 - x^{2})^{1.5} + 6 (arcsin (0.5 x) - 0.25 sin (4 arcsin (0.5 x))) + C

Solution steps

\int (4 - x^{2})^{1.5} d x

Apply Integration By Parts

: x (4 - x^{2})^{1.5} - \int - 3 x^{2} 4 - x^{2} d x

= x (4 - x^{2})^{1.5} - \int - 3 x^{2} 4 - x^{2} d x

\int - 3 x^{2} 4 - x^{2} d x = - 6 (arcsin (\frac{1}{2} x) - \frac{1}{4} sin (4 arcsin (\frac{1}{2} x)))

= x (4 - x^{2})^{1.5} - (- 6 (arcsin (\frac{1}{2} x) - \frac{1}{4} sin (4 arcsin (\frac{1}{2} x))))

Simplify

= x (4 - x^{2})^{1.5} + 6 (arcsin (0.5 x) - 0.25 sin (4 arcsin (0.5 x)))

Add a constant to the solution

= x (4 - x^{2})^{1.5} + 6 (arcsin (0.5 x) - 0.25 sin (4 arcsin (0.5 x))) + C

(1 - x^{2})^{3}

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

\frac{e ^{\frac{1}{y}}}{y}

\frac{1}{( sin ( x ) cos ^{2} ( x ) )}

x^{3} - x^{2}

What is the integral of (4-x^2)^{1.5} ?
The integral of (4-x^2)^{1.5} is x(4-x^2)^{1.5}+6(arcsin(0.5x)-0.25sin(4arcsin(0.5x)))+C