What is the integral of 15(tan(x))(ln(cos(x))) ?

The integral of 15(tan(x))(ln(cos(x))) is -15/2 ln^2(cos(x))+C

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integral of 15(tan(x))(ln(cos(x)))

\int 15 (tan (x)) (ln (cos (x))) d x

- \frac{15}{2} ln^{2} (cos (x)) + C

Solution steps

\int 15 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

= 15 \cdot \int tan (x) ln (cos (x)) d x

Apply u-substitution

= 15 \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

= 15 (- \int \frac{ln ( u )}{u} d u)

Apply u-substitution

= 15 (- \int v d v)

Apply the Power Rule

= 15 (- \frac{v ^{2}}{2})

Substitute back

= 15 (- \frac{ln ^{2} ( cos ( x ) )}{2})

Simplify

15 (- \frac{ln ^{2} ( cos ( x ) )}{2}) : - \frac{15}{2} ln^{2} (cos (x))

= - \frac{15}{2} ln^{2} (cos (x))

Add a constant to the solution

= - \frac{15}{2} ln^{2} (cos (x)) + C

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

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

t an g e n t y = 4.2 x - x^{2}

\int \frac{700 x}{( x + 1 ) ^{\frac{1}{3}}} d x

x \to 0 lim (\frac{e ^{x} - 1}{9 x})

What is the integral of 15(tan(x))(ln(cos(x))) ?
The integral of 15(tan(x))(ln(cos(x))) is -15/2 ln^2(cos(x))+C