What is the integral of (9(csc(t))^2)/(cot(t)) ?

The integral of (9(csc(t))^2)/(cot(t)) is 9ln|tan(t)|+C

Popular >

integral of (9(csc(t))^2)/(cot(t))

\int \frac{9 ( csc ( t ) ) ^{2}}{cot ( t )} d t

9 ln ∣ tan (t) ∣ + C

Solution steps

\int \frac{9 ( csc ( t ) ) ^{2}}{cot ( t )} d t

Take the constant out:

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

= 9 \cdot \int \frac{( csc ( t ) ) ^{2}}{cot ( t )} d t

Rewrite using trig identities

= 9 \cdot \int \frac{sec ( t )}{sin ( t )} d t

Apply Trigonometric Substitution

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

= 9 \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 9 ln ∣ u ∣

Substitute back

u = tan (t)

= 9 ln ∣ tan (t) ∣

Add a constant to the solution

= 9 ln ∣ tan (t) ∣ + C

x \to 0 lim (x^{5} - 6 x^{4} + 7)

\int x 2 x^{2} + 1 d x

\frac{d}{d x} (x \cdot arctan (x))

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

x \to - 0.1 lim (x^{3} + 6 x^{2} + x)

What is the integral of (9(csc(t))^2)/(cot(t)) ?
The integral of (9(csc(t))^2)/(cot(t)) is 9ln|tan(t)|+C