What is the integral of cos^2(x)+4/(sqrt(4-x^2)) ?

The integral of cos^2(x)+4/(sqrt(4-x^2)) is 1/2 (x+1/2 sin(2x))+4arcsin(1/2 x)+C

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integral of cos^2(x)+4/(sqrt(4-x^2))

\int cos^{2} (x) + \frac{4}{4 - x ^{2}} d x

\frac{1}{2} (x + \frac{1}{2} sin (2 x)) + 4 arcsin (\frac{1}{2} x) + C

Solution steps

\int cos^{2} (x) + \frac{4}{4 - x ^{2}} 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 cos^{2} (x) d x + \int \frac{4}{4 - x ^{2}} d x

\int cos^{2} (x) d x = \frac{1}{2} (x + \frac{1}{2} sin (2 x))

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

= \frac{1}{2} (x + \frac{1}{2} sin (2 x)) + 4 arcsin (\frac{1}{2} x)

Add a constant to the solution

= \frac{1}{2} (x + \frac{1}{2} sin (2 x)) + 4 arcsin (\frac{1}{2} x) + C

x \to 1 + lim (\frac{x ^{4} - 1}{x - 1})

n = 1 \sum \infty \frac{8 n}{- 2 n + 9}

y^{^{''}} + 5 y^{^{'}} - 6 y = 22 + 18 x - 18 x^{2}

\frac{d}{d x} (f (x) (4 sin (x^{2} - 1)))

\int x^{2} x^{2} - 49 d x

What is the integral of cos^2(x)+4/(sqrt(4-x^2)) ?
The integral of cos^2(x)+4/(sqrt(4-x^2)) is 1/2 (x+1/2 sin(2x))+4arcsin(1/2 x)+C