What is the integral of (sin(θ)+cos(θ))^2 ?

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

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integral of (sin(θ)+cos(θ))^2

\int (sin (θ) + cos (θ))^{2} d θ

θ - \frac{1}{2} cos (2 θ) + C

Solution steps

\int (sin (θ) + cos (θ))^{2} d θ

Rewrite using trig identities

= \int 1 + sin (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

= \int 1 d θ + \int sin (2 θ) d θ

\int 1 d θ = θ

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

= θ - \frac{1}{2} cos (2 θ)

Add a constant to the solution

= θ - \frac{1}{2} cos (2 θ) + C

\int \frac{1}{2 cos ( x ) + 3} d x

\int \frac{5 x ^{4}}{x ^{5} + 1} d x

\int 2 e^{x} + 4 d x

\int \frac{x ^{\frac{3}{2}} - x ^{\frac{1}{3}}}{6 x ^{\frac{1}{4}}} d x

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