What is the integral of 5cos(pix-3) ?

The integral of 5cos(pix-3) is 5/pi sin(pix-3)+C

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integral of 5cos(pix-3)

\int 5 cos (π x - 3) d x

\frac{5}{π} sin (π x - 3) + C

Solution steps

\int 5 cos (π x - 3) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 5 \cdot \int cos (π x - 3) d x

Rewrite using trig identities

= 5 \cdot \int cos (π x) cos (3) + sin (π x) sin (3) 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

= 5 (\int cos (π x) cos (3) d x + \int sin (π x) sin (3) d x)

\int cos (π x) cos (3) d x = cos (3) \frac{1}{π} sin (π x)

\int sin (π x) sin (3) d x = - \frac{1}{π} sin (3) cos (π x)

= 5 (cos (3) \frac{1}{π} sin (π x) - \frac{1}{π} sin (3) cos (π x))

Simplify

5 (cos (3) \frac{1}{π} sin (π x) - \frac{1}{π} sin (3) cos (π x)) : \frac{5}{π} sin (π x - 3)

= \frac{5}{π} sin (π x - 3)

Add a constant to the solution

= \frac{5}{π} sin (π x - 3) + C

\frac{4 x}{x ^{2} + 2}

\frac{\partial}{\partial x} (x (10 - x - y))

\frac{d ^{2} y}{d x ^{2}} - 4 \frac{d y}{d x} = 12 cos (2 x)

\int \frac{6 - 6 x}{1 - x} d x

y = 3 x^{2} + 1, (0, - 1)

What is the integral of 5cos(pix-3) ?
The integral of 5cos(pix-3) is 5/pi sin(pix-3)+C