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

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

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integral of (sin(x)+cos(x))^2

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

x - \frac{1}{2} cos (2 x) + C

Solution steps

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

Rewrite using trig identities

= \int 1 + sin (2 x) 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 1 d x + \int sin (2 x) d x

\int 1 d x = x

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

= x - \frac{1}{2} cos (2 x)

Add a constant to the solution

= x - \frac{1}{2} cos (2 x) + C

\frac{d}{d x} (\frac{x - 3}{6 x - 5})

x \to 2 lim (\frac{1}{2 - x})

\frac{\partial}{\partial y} (e^{- x} cos (y))

(2, 5), (3, 1)

\int 0.33 e^{- 0.33 y} d y

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