What is the integral of cot(m)xcsc^2(m)x ?

The integral of cot(m)xcsc^2(m)x is (csc^2(m))/3 x^3cot(m)+C

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integral of cot(m)xcsc^2(m)x

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

\frac{csc ^{2} ( m )}{3} x^{3} cot (m) + C

Solution steps

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

Take the constant out:

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

= cot (m) csc^{2} (m) \cdot \int xx d x

Simplify

xx : x^{2}

= cot (m) csc^{2} (m) \cdot \int x^{2} d x

Apply the Power Rule

: \frac{x ^{3}}{3}

= cot (m) csc^{2} (m) \frac{x ^{3}}{3}

Simplify

cot (m) csc^{2} (m) \frac{x ^{3}}{3} : \frac{csc ^{2} ( m )}{3} x^{3} cot (m)

= \frac{csc ^{2} ( m )}{3} x^{3} cot (m)

Add a constant to the solution

= \frac{csc ^{2} ( m )}{3} x^{3} cot (m) + C

f (x) = 2 x^{3}, at x = - 1

\int sin (\frac{x}{5}) d x

a x^{3}, at x = - 5

y = 3 arctan (x - 1 + x^{2})

\frac{\partial}{\partial y} (y^{3} cos (x + y))

What is the integral of cot(m)xcsc^2(m)x ?
The integral of cot(m)xcsc^2(m)x is (csc^2(m))/3 x^3cot(m)+C