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

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

Popular >

integral of tan(x)ln(cos(x))

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

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

Solution steps

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

Apply u-substitution

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

= \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

= - \int v d v

Apply the Power Rule

: \frac{v ^{2}}{2}

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

Substitute back

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

Add a constant to the solution

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

\int \frac{x ^{2}}{x ^{2} + 4} d x

y = x^{2} - 1, y = 2 x - 1, y = x + 1

y = \frac{2}{1 + x ^{2}}, (3, 0.2)

x (\frac{d y}{d x}) - y = x^{5} + 1

f (x) = x^{2} - 5 x

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