What is the integral of xcsc(4)x^2 ?

The integral of xcsc(4)x^2 is 1/4 csc(4)x^4+C

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integral of xcsc(4)x^2

\int x csc (4) x^{2} d x

\frac{1}{4} csc (4) x^{4} + C

Solution steps

\int x csc (4) x^{2} d x

Take the constant out:

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

= csc (4) \cdot \int x x^{2} d x

Simplify

x x^{2} : x^{3}

= csc (4) \cdot \int x^{3} d x

Apply the Power Rule

: \frac{x ^{4}}{4}

= csc (4) \frac{x ^{4}}{4}

Simplify

csc (4) \frac{x ^{4}}{4} : \frac{1}{4} csc (4) x^{4}

= \frac{1}{4} csc (4) x^{4}

Add a constant to the solution

= \frac{1}{4} csc (4) x^{4} + C

\frac{d}{d x} (\frac{1}{2} cos^{2} (5 x))

f (x) = x^{3}

\int_{- 2}^{1} (x^{3} + 5) d x

y = x^{3} + \frac{1}{12 x}

y = x, 2 x 64 - x^{2}

What is the integral of xcsc(4)x^2 ?
The integral of xcsc(4)x^2 is 1/4 csc(4)x^4+C