What is the integral of (cos(θ))/(sqrt(4-sin^2(θ))) ?

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

Popular >

integral of (cos(θ))/(sqrt(4-sin^2(θ)))

\int \frac{cos ( θ )}{4 - sin ^{2} ( θ )} d θ

arcsin (\frac{1}{2} sin (θ)) + C

Solution steps

\int \frac{cos ( θ )}{4 - sin ^{2} ( θ )} d θ

Apply u-substitution

: \int \frac{1}{4 - u ^{2}} d u

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

Apply Trigonometric Substitution

: \int 1 d v

= \int 1 d v

Integral of a constant:

\int a d x = a x

= 1 \cdot v

Substitute back

= 1 \cdot arcsin (\frac{1}{2} sin (θ))

Simplify

= arcsin (\frac{1}{2} sin (θ))

Add a constant to the solution

= arcsin (\frac{1}{2} sin (θ)) + C

\int 6 x - 9 x^{2} + C d x

\int sin^{5} (2 x) cos^{\frac{3}{2}} (2 x) d x

\int \frac{sec ^{2} ( x )}{csc ^{2} ( x )} d x

\int x csc^{2} (x) cot (x) d x

\int \frac{3 + sin ( x )}{cos ^{2} ( x )} d x

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