What is the integral of csc^2(xco)t^2x ?

The integral of csc^2(xco)t^2x is t^2 1/(c^2o^2)(-coxcot(cox)+ln|sin(cox)|)+C

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integral of csc^2(xco)t^2x

\int csc^{2} (x co) t^{2} x d x

t^{2} \frac{1}{c ^{2} o ^{2}} (- co x cot (co x) + ln ∣ sin (co x) ∣) + C

Solution steps

\int csc^{2} (x co) t^{2} x d x

Take the constant out:

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

= t^{2} \cdot \int csc^{2} (co x) x d x

Apply u-substitution

: \int \frac{u csc ^{2} ( u )}{c ^{2} o ^{2}} d u

= t^{2} \cdot \int \frac{u csc ^{2} ( u )}{c ^{2} o ^{2}} d u

Take the constant out:

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

= t^{2} \frac{1}{c ^{2} o ^{2}} \cdot \int u csc^{2} (u) d u

Apply Integration By Parts

: - u cot (u) - \int - cot (u) d u

= t^{2} \frac{1}{c ^{2} o ^{2}} (- u cot (u) - \int - cot (u) d u)

\int - cot (u) d u = - ln ∣ sin (u) ∣

= t^{2} \frac{1}{c ^{2} o ^{2}} (- u cot (u) - (- ln ∣ sin (u) ∣))

Substitute back

u = co x

= t^{2} \frac{1}{c ^{2} o ^{2}} (- co x cot (co x) - (- ln ∣ sin (co x) ∣))

Simplify

= t^{2} \frac{1}{c ^{2} o ^{2}} (- co x cot (co x) + ln ∣ sin (co x) ∣)

Add a constant to the solution

= t^{2} \frac{1}{c ^{2} o ^{2}} (- co x cot (co x) + ln ∣ sin (co x) ∣) + C

y = - 3 x^{3} + x^{2} + 10 x, x = - \frac{5}{3}, x = 2

x \to a lim (x + x - 4)

\frac{d}{d x} (x cos (x) + sin (x))

x \to c lim (5 + 3 (- 2))

\int (2 x + 3) cos (x^{2} + 3 x) d x

What is the integral of csc^2(xco)t^2x ?
The integral of csc^2(xco)t^2x is t^2 1/(c^2o^2)(-coxcot(cox)+ln|sin(cox)|)+C