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

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

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

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

\frac{1}{2} (x - \frac{1}{14} sin (14 x)) - sin (x) + C

Solution steps

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

\int sin^{2} (7 x) d x = \frac{1}{2} (x - \frac{1}{14} sin (14 x))

\int cos (x) d x = sin (x)

= \frac{1}{2} (x - \frac{1}{14} sin (14 x)) - sin (x)

Add a constant to the solution

= \frac{1}{2} (x - \frac{1}{14} sin (14 x)) - sin (x) + C

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