What is the integral of (4x+3)/(sqrt(1-x^2)) ?

The integral of (4x+3)/(sqrt(1-x^2)) is -4sqrt(1-x^2)+3arcsin(x)+C

integral of (4x+3)/(sqrt(1-x^2))

\int \frac{4 x + 3}{1 - x ^{2}} d x

- 4 1 - x^{2} + 3 arcsin (x) + C

Solution steps

\int \frac{4 x + 3}{1 - x ^{2}} d x

Expand

\frac{4 x + 3}{1 - x ^{2}} : \frac{4 x}{1 - x ^{2}} + \frac{3}{1 - x ^{2}}

= \int \frac{4 x}{1 - x ^{2}} + \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 \frac{4 x}{1 - x ^{2}} d x + \int \frac{3}{1 - x ^{2}} d x

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

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

= - 4 1 - x^{2} + 3 arcsin (x)

Add a constant to the solution

= - 4 1 - x^{2} + 3 arcsin (x) + C

\frac{d}{d x} (sin (4 x + 7 x^{4}) + e^{1 - x^{2}})

\int \frac{x ^{2} + 24 x - 9}{x ^{3} - 9 x} d x

x \to \frac{π}{2} lim (- cos (x))

d er i v a t i v e y = \frac{6 x ^{2} + 6 x + 2}{x}

d er i v a t i v e 5 cos (x)

What is the integral of (4x+3)/(sqrt(1-x^2)) ?
The integral of (4x+3)/(sqrt(1-x^2)) is -4sqrt(1-x^2)+3arcsin(x)+C