What is the integral of (sin(7x)+cos(7x))^2 ?

The integral of (sin(7x)+cos(7x))^2 is x-1/14 cos(14x)+C

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integral of (sin(7x)+cos(7x))^2

\int (sin (7 x) + cos (7 x))^{2} d x

x - \frac{1}{14} cos (14 x) + C

Solution steps

\int (sin (7 x) + cos (7 x))^{2} d x

Rewrite using trig identities

= \int 1 + sin (14 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 (14 x) d x

\int 1 d x = x

\int sin (14 x) d x = - \frac{1}{14} cos (14 x)

= x - \frac{1}{14} cos (14 x)

Add a constant to the solution

= x - \frac{1}{14} cos (14 x) + C

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What is the integral of (sin(7x)+cos(7x))^2 ?
The integral of (sin(7x)+cos(7x))^2 is x-1/14 cos(14x)+C