What is the integral of 2cos(x)-3/(sqrt(1-x^2)) ?

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

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integral of 2cos(x)-3/(sqrt(1-x^2))

\int 2 cos (x) - \frac{3}{1 - x ^{2}} d x

2 sin (x) - 3 arcsin (x) + C

Solution steps

\int 2 cos (x) - \frac{3}{1 - 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 2 cos (x) d x - \int \frac{3}{1 - x ^{2}} d x

\int 2 cos (x) d x = 2 sin (x)

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

= 2 sin (x) - 3 arcsin (x)

Add a constant to the solution

= 2 sin (x) - 3 arcsin (x) + C

f (x) = 2 x^{2}, at x = 3

x \to 3 + lim (\frac{x + 3}{x ^{2} - 9})

\frac{d}{d x} (x^{4} + 5 x y^{3})

\int \frac{2}{t} d t

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

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