What is the integral of 7cos(x)-8/(sqrt(1-x^2)) ?

The integral of 7cos(x)-8/(sqrt(1-x^2)) is 7sin(x)-8arcsin(x)+C

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integral of 7cos(x)-8/(sqrt(1-x^2))

\int 7 cos (x) - \frac{8}{1 - x ^{2}} d x

7 sin (x) - 8 arcsin (x) + C

Solution steps

\int 7 cos (x) - \frac{8}{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 7 cos (x) d x - \int \frac{8}{1 - x ^{2}} d x

\int 7 cos (x) d x = 7 sin (x)

\int \frac{8}{1 - x ^{2}} d x = 8 arcsin (x)

= 7 sin (x) - 8 arcsin (x)

Add a constant to the solution

= 7 sin (x) - 8 arcsin (x) + C

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What is the integral of 7cos(x)-8/(sqrt(1-x^2)) ?
The integral of 7cos(x)-8/(sqrt(1-x^2)) is 7sin(x)-8arcsin(x)+C