What is the integral of cos(200tn) ?

The integral of cos(200tn) is 1/(200n)sin(200tn)+C

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integral of cos(200tn)

\int cos (200 t n) d t

\frac{1}{200 n} sin (200 t n) + C

Solution steps

\int cos (200 t n) d t

Apply u-substitution

: \int \frac{cos ( u )}{200 n} d u

= \int \frac{cos ( u )}{200 n} d u

Take the constant out:

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

= \frac{1}{200 n} \cdot \int cos (u) d u

Use the common integral:

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

= \frac{1}{200 n} sin (u)

Substitute back

u = 200 t n

= \frac{1}{200 n} sin (200 t n)

Add a constant to the solution

= \frac{1}{200 n} sin (200 t n) + C

\int sin (20 x) cos (17 x) d x

x^{2} y^{^{'}} = y^{2} + 5 x y + 4 x^{2}

\frac{d}{d x} ((4 x^{2} - 8 x + 8) e^{- 6 x})

x = t sin (t)

8 e^{t}

What is the integral of cos(200tn) ?
The integral of cos(200tn) is 1/(200n)sin(200tn)+C