What is the integral of cos(at) ?

The integral of cos(at) is 1/a sin(at)+C

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integral of cos(at)

\int cos (a t) d t

\frac{1}{a} sin (a t) + C

Solution steps

\int cos (a t) d t

Apply u-substitution

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

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

Take the constant out:

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

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

Use the common integral:

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

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

Substitute back

u = a t

= \frac{1}{a} sin (a t)

Add a constant to the solution

= \frac{1}{a} sin (a t) + C

\int_{0}^{1} y e^{y} d y

x \to 0 lim (\frac{( x + 3 ) ^{2} - 9}{x})

x (10 - 2 x) (16 - 2 x)

y^{^{'}} + 2 y = e^{x}

\frac{\partial}{\partial x} (z^{3})