What is the integral of-((csc(x))^2)/(cot(x)) ?

The integral of-((csc(x))^2)/(cot(x)) is -ln|tan(x)|+C

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integral of-((csc(x))^2)/(cot(x))

\int - \frac{( csc ( x ) ) ^{2}}{cot ( x )} d x

- ln ∣ tan (x) ∣ + C

Solution steps

\int - \frac{( csc ( x ) ) ^{2}}{cot ( x )} d x

Take the constant out:

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

= - \int \frac{( csc ( x ) ) ^{2}}{cot ( x )} d x

Rewrite using trig identities

= - \int \frac{sec ( x )}{sin ( x )} d x

Apply Trigonometric Substitution

: \int \frac{1}{u} d u

= - \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= - ln ∣ u ∣

Substitute back

u = tan (x)

= - ln ∣ tan (x) ∣

Add a constant to the solution

= - ln ∣ tan (x) ∣ + C

y = (5 x^{2} - 6 x)^{- 2}

\int \frac{sec ( x ) tan ( x )}{sec ( x ) - 6} d x

\int x^{2} e^{x} sin (x) d x

\int \frac{1}{x ( x - 3 ) ^{2}} d x

\frac{\partial}{\partial x} (x y + x e^{\frac{1}{y}})

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