What is the integral of ln(cos(w))tan(w) ?

The integral of ln(cos(w))tan(w) is -(ln^2(cos(w)))/2+C

integral of ln(cos(w))tan(w)

\int ln (cos (w)) tan (w) d w

- \frac{ln ^{2} ( cos ( w ) )}{2} + C

Solution steps

\int ln (cos (w)) tan (w) d w

Apply u-substitution

= \int - \frac{ln ( u )}{u} d u

Take the constant out:

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

= - \int \frac{ln ( u )}{u} d u

Apply u-substitution

= - \int v d v

Apply the Power Rule

= - \frac{v ^{2}}{2}

Substitute back

= - \frac{ln ^{2} ( cos ( w ) )}{2}

Add a constant to the solution

= - \frac{ln ^{2} ( cos ( w ) )}{2} + C

(2 x y) d x + (1 - x^{2}) d y = 0

x \to \infty lim (\frac{ln ( x ) + x ^{3}}{e ^{- x}})

n = 0 \sum \infty \frac{9}{3 ^{n - 1}}

x \to 2 lim (x^{2} - 43 - x + 7)

\frac{d}{d x} (ln (x + \frac{1}{x}))

What is the integral of ln(cos(w))tan(w) ?
The integral of ln(cos(w))tan(w) is -(ln^2(cos(w)))/2+C