What is the integral of cos(pix)+3sin(x/3) ?

The integral of cos(pix)+3sin(x/3) is 1/pi sin(pix)-9cos(x/3)+C

Popular >

integral of cos(pix)+3sin(x/3)

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

\frac{1}{π} sin (π x) - 9 cos (\frac{x}{3}) + C

Solution steps

\int cos (π x) + 3 sin (\frac{x}{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

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

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

\int 3 sin (\frac{x}{3}) d x = - 9 cos (\frac{x}{3})

= \frac{1}{π} sin (π x) - 9 cos (\frac{x}{3})

Add a constant to the solution

= \frac{1}{π} sin (π x) - 9 cos (\frac{x}{3}) + C

\int e^{4 x^{2}} 8 x d x

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

\int \frac{2}{200 + t} d t

\int (x + \frac{1}{x})^{2} d x

\int \frac{6 x - 3}{4 x ^{2} - 4 x + 1} d x

What is the integral of cos(pix)+3sin(x/3) ?
The integral of cos(pix)+3sin(x/3) is 1/pi sin(pix)-9cos(x/3)+C