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

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

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

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

x + C

Solution steps

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

Rewrite using trig identities

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

cos^{2} (x) = (cos (x)),

assuming

cos (x) \geq 0

= \int \frac{cos ( x )}{cos ( x )} d x

Simplify

= \int 1 d x

Integral of a constant:

\int a d x = a x

= 1 \cdot x

Simplify

= x

Add a constant to the solution

= x + C

\int (\frac{1}{x ^{8}}) d x

\frac{d}{d x} (25 - x)

x \to 0 lim (2 x + 1 - 1)

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