What is the integral of (sin(t))/(cos(t)) ?

The integral of (sin(t))/(cos(t)) is -ln|cos(t)|+C

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integral of (sin(t))/(cos(t))

\int \frac{sin ( t )}{cos ( t )} d t

- ln ∣ cos (t) ∣ + C

Solution steps

\int \frac{sin ( t )}{cos ( t )} d t

Apply u-substitution

: \int - \frac{1}{u} d u

= \int - \frac{1}{u} d u

Take the constant out:

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

= - \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= - ln ∣ u ∣

Substitute back

u = cos (t)

= - ln ∣ cos (t) ∣

Add a constant to the solution

= - ln ∣ cos (t) ∣ + C

x \to 2 lim (2 x^{2} - 2)

7 cos (9 x), 7 - 7 cos (9 x)

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

\int (2 x e^{x^{2}}) d x

y = x^{3}, y = x^{2} - 2 x, [0, 1]

What is the integral of (sin(t))/(cos(t)) ?
The integral of (sin(t))/(cos(t)) is -ln|cos(t)|+C