What is the integral of cos(my) ?

The integral of cos(my) is 1/m sin(my)+C

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integral of cos(my)

\int cos (m y) d y

\frac{1}{m} sin (m y) + C

Solution steps

\int cos (m y) d y

Apply u-substitution

: \int \frac{cos ( u )}{m} d u

= \int \frac{cos ( u )}{m} d u

Take the constant out:

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

= \frac{1}{m} \cdot \int cos (u) d u

Use the common integral:

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

= \frac{1}{m} sin (u)

Substitute back

u = m y

= \frac{1}{m} sin (m y)

Add a constant to the solution

= \frac{1}{m} sin (m y) + C

1 - 2 x

n = 1 \sum \infty \frac{2 n}{n !}

\int \frac{6 x ^{3} + 2 x ^{2} - 47 x - 9}{x ^{2} - 9} d x

f (x) = 7 x - 2 x^{2}, (- 1, - 9)

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