What is the integral of (ln(sin(x)))/(tan(x)) ?

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

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integral of (ln(sin(x)))/(tan(x))

\int \frac{ln ( sin ( x ) )}{tan ( x )} d x

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

Solution steps

\int \frac{ln ( sin ( x ) )}{tan ( x )} d x

Rewrite using trig identities

= \int ln (sin (x)) cot (x) d x

Apply u-substitution

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

= \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} ( sin ( x ) )}{2}

Add a constant to the solution

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

\frac{x}{9} - \frac{9}{x}

f (x) = e^{c o s (x)}

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

\int (5 - 4 e^{x} + \frac{3}{x ^{2}}) d x

h \to 0 lim (\frac{( 2 h ^{2} + 6 h )}{h})

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