What is the integral of-sqrt(2)-2cos(3/4 pix) ?

The integral of-sqrt(2)-2cos(3/4 pix) is -sqrt(2)x-8/(3pi)sin((3pi)/4 x)+C

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integral of-sqrt(2)-2cos(3/4 pix)

\int - 2 - 2 cos (\frac{3}{4} π x) d x

- 2 x - \frac{8}{3 π} sin (\frac{3 π}{4} x) + C

Solution steps

\int - 2 - 2 cos (\frac{3}{4} π x) d x

\frac{3}{4} = 3 \cdot \frac{1}{4}

= \int - 2 - 2 cos (3 \cdot \frac{1}{4} π 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 2 d x - \int 2 cos (3 \cdot \frac{1}{4} π x) d x

\int 2 d x = 2 x

\int 2 cos (3 \cdot \frac{1}{4} π x) d x = \frac{8}{3 π} sin (\frac{3 π}{4} x)

= - 2 x - \frac{8}{3 π} sin (\frac{3 π}{4} x)

Add a constant to the solution

= - 2 x - \frac{8}{3 π} sin (\frac{3 π}{4} x) + C

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What is the integral of-sqrt(2)-2cos(3/4 pix) ?
The integral of-sqrt(2)-2cos(3/4 pix) is -sqrt(2)x-8/(3pi)sin((3pi)/4 x)+C