What is the integral of bcos(at) ?

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

Popular >

integral of bcos(at)

\int b cos (a t) d t

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

Solution steps

\int b cos (a t) d t

Take the constant out:

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

= b \cdot \int cos (a t) d t

Apply u-substitution

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

= b \cdot \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

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

Use the common integral:

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

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

Substitute back

u = a t

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

Add a constant to the solution

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

\int 5 x sin (2 x^{2}) d x

\int \frac{1}{500} e^{- \frac{x}{500}} d x

\int \frac{x + 2}{x ^{2} + 5 x + 4} d x

\int \frac{3}{4 x ^{2} + 16} d x

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