What is the integral of 11(tan(x))(ln(cos(x))) ?

The integral of 11(tan(x))(ln(cos(x))) is -11/2 ln^2(cos(x))+C

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integral of 11(tan(x))(ln(cos(x)))

\int 11 (tan (x)) (ln (cos (x))) d x

- \frac{11}{2} ln^{2} (cos (x)) + C

Solution steps

\int 11 tan (x) ln (cos (x)) d x

Take the constant out:

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

= 11 \cdot \int tan (x) ln (cos (x)) d x

Apply u-substitution

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

= 11 \cdot \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

= 11 (- \int \frac{ln ( u )}{u} d u)

Apply u-substitution

: \int v d v

= 11 (- \int v d v)

Apply the Power Rule

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

= 11 (- \frac{v ^{2}}{2})

Substitute back

= 11 (- \frac{ln ^{2} ( cos ( x ) )}{2})

Simplify

11 (- \frac{ln ^{2} ( cos ( x ) )}{2}) : - \frac{11}{2} ln^{2} (cos (x))

= - \frac{11}{2} ln^{2} (cos (x))

Add a constant to the solution

= - \frac{11}{2} ln^{2} (cos (x)) + C

\frac{\frac{1}{7}}{s ^{2} + \frac{19980}{7}}

\int t^{- \frac{1}{2}} (t^{4} + 2 t^{2} - 1) d t

\int sin (s) d s

- 4 t^{2} + 16 t + 9

\frac{\partial}{\partial x} (4 x (2 + y)^{- 1})

What is the integral of 11(tan(x))(ln(cos(x))) ?
The integral of 11(tan(x))(ln(cos(x))) is -11/2 ln^2(cos(x))+C