What is the integral of cot^3(x ?

The integral of cot^3(x is (x^2cot^3(d))/2+C

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integral of cot^3(x

\int cot^{3} (d) x d x

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

Solution steps

\int cot^{3} (d) x d x

Take the constant out:

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

= cot^{3} (d) \cdot \int x d x

Apply the Power Rule

: \frac{x ^{2}}{2}

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

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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

Add a constant to the solution

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

\int (cot^{2} (x) + 1)^{2} csc^{2} (x) d x

\int x (2 x + 3)^{7} d x

\int a x^{7} d x

\int \frac{cot ( t ) csc ( t )}{csc ^{7} ( t )} d t

\int - tan (2 x + 1) ln (cos (2 x + 1)) d x