What is the integral of (1-sin^2(θ)) ?

The integral of (1-sin^2(θ)) is 1/2 (θ+1/2 sin(2θ))+C

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integral of (1-sin^2(θ))

\int (1 - sin^{2} (θ)) d θ

\frac{1}{2} (θ + \frac{1}{2} sin (2 θ)) + C

Solution steps

\int 1 - sin^{2} (θ) d θ

Rewrite using trig identities

= \int \frac{1 + cos ( 2 θ )}{2} d θ

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{2} \cdot \int 1 + cos (2 θ) d θ

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \frac{1}{2} (\int 1 d θ + \int cos (2 θ) d θ)

\int 1 d θ = θ

\int cos (2 θ) d θ = \frac{1}{2} sin (2 θ)

= \frac{1}{2} (θ + \frac{1}{2} sin (2 θ))

Add a constant to the solution

= \frac{1}{2} (θ + \frac{1}{2} sin (2 θ)) + C

\frac{d}{d x} ((2 x^{2} - 1)^{3} (x^{4} + 3)^{5})

75 (1 - \frac{t}{24})^{2}

\int t sec^{2} (4 t) d t

y = x^{3} (2 x - 1)^{7}

\int x^{8} (x^{9} - 10)^{7} d x

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