What is the integral of cot(5/8)x 5/8 ?

The integral of cot(5/8)x 5/8 is 5/16 cot(5/8)x^2+C

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integral of cot(5/8)x 5/8

\int cot (\frac{5}{8}) x \frac{5}{8} d x

\frac{5}{16} cot (\frac{5}{8}) x^{2} + C

Solution steps

\int cot (\frac{5}{8}) x \frac{5}{8} d x

Take the constant out:

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

= cot (\frac{5}{8}) \frac{5}{8} \cdot \int x d x

Apply the Power Rule

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

= cot (\frac{5}{8}) \frac{5}{8} \cdot \frac{x ^{2}}{2}

Simplify

cot (\frac{5}{8}) \frac{5}{8} \cdot \frac{x ^{2}}{2} : \frac{5}{16} cot (\frac{5}{8}) x^{2}

= \frac{5}{16} cot (\frac{5}{8}) x^{2}

Add a constant to the solution

= \frac{5}{16} cot (\frac{5}{8}) x^{2} + C

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What is the integral of cot(5/8)x 5/8 ?
The integral of cot(5/8)x 5/8 is 5/16 cot(5/8)x^2+C