What is the integral of cos(nt) ?

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

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integral of cos(nt)

\int cos (n t) d t

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

Solution steps

\int cos (n t) d t

Apply u-substitution

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

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

Take the constant out:

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

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

Use the common integral:

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

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

Substitute back

u = n t

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

Add a constant to the solution

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

\frac{d}{d x} (x^{3} (x - 4))

91 - 90 e^{- 0.2 t}

\frac{6}{s} + 16 \cdot \frac{1}{s ^{2} + 16}

f (x) = \frac{2}{4 - x}, at x = - 1

(sin^{2} (x))^{^{'}}