What is the integral of csc^2(1/3)x ?

The integral of csc^2(1/3)x is (csc^2(1/3)x^2)/2+C

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integral of csc^2(1/3)x

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

\frac{csc ^{2} ( \frac{1}{3} ) x ^{2}}{2} + C

Solution steps

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

Take the constant out:

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

= csc^{2} (\frac{1}{3}) \cdot \int x d x

Apply the Power Rule

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

= csc^{2} (\frac{1}{3}) \frac{x ^{2}}{2}

Multiply fractions:

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

= \frac{csc ^{2} ( \frac{1}{3} ) x ^{2}}{2}

Add a constant to the solution

= \frac{csc ^{2} ( \frac{1}{3} ) x ^{2}}{2} + C

\frac{1}{1 + t}

\frac{2 x}{x ^{4} + 1}

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

x \to 0 + lim ((1 + 4 x)^{\frac{5}{x}})

\frac{d y}{d x}, y^{5} = x^{7}

What is the integral of csc^2(1/3)x ?
The integral of csc^2(1/3)x is (csc^2(1/3)x^2)/2+C