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Popular >

integral of csc^2(5y)

Solution

\int csc^{2} (5 y) d y

Solution

- \frac{1}{5} cot (5 y) + C

Solution steps

\int csc^{2} (5 y) d y

Apply u-substitution

: \int csc^{2} (u) \frac{1}{5} d u

= \int csc^{2} (u) \frac{1}{5} d u

Take the constant out:

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

= \frac{1}{5} \cdot \int csc^{2} (u) d u

Use the common integral:

\int csc^{2} (u) d u = - cot (u)

= \frac{1}{5} (- cot (u))

Substitute back

u = 5 y

= \frac{1}{5} (- cot (5 y))

Simplify

= - \frac{1}{5} cot (5 y)

Add a constant to the solution

= - \frac{1}{5} cot (5 y) + C

Popular Examples

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y = \frac{1}{x}, y = \frac{1}{x ^{2}}, x = 3

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

integral of (xe^x)/((x+1)^2)

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derivative of (5x^2-8xe^x)

\frac{d}{d x} ((5 x^{2} - 8 x) e^{x})

x^{''}-0x^'+x=0

x^{^{''}} - 0 x^{^{'}} + x = 0

Frequently Asked Questions (FAQ)

What is the integral of csc^2(5y) ?
The integral of csc^2(5y) is -1/5 cot(5y)+C