What is the integral of (sin(x))(sec(x)) ?

The integral of (sin(x))(sec(x)) is -ln|cos(x)|+C

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integral of (sin(x))(sec(x))

\int (sin (x)) (sec (x)) d x

- ln ∣ cos (x) ∣ + C

Solution steps

\int sin (x) sec (x) d x

Rewrite using trig identities

= \int \frac{sin ( x )}{cos ( x )} d x

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 (x)

= - ln ∣ cos (x) ∣

Add a constant to the solution

= - ln ∣ cos (x) ∣ + C

- \frac{x}{y}

\int e^{- 2 y} d y

x \to a lim ((x + 2 x^{3})^{4})

\frac{d}{d x} (900 x - \frac{1}{3} x^{3} + 2500)

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

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