What is the integral of csc(7x) ?

The integral of csc(7x) is 1/7 ln|tan((7x)/2)|+C

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integral of csc(7x)

\int csc (7 x) d x

\frac{1}{7} ln tan (\frac{7 x}{2}) + C

Solution steps

\int csc (7 x) d x

Apply u-substitution

= \int csc (u) \frac{1}{7} d u

Take the constant out:

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

= \frac{1}{7} \cdot \int csc (u) d u

Apply u-substitution

= \frac{1}{7} \cdot \int \frac{1}{v} d v

Use the common integral:

\int \frac{1}{v} d v = ln (∣ v ∣)

= \frac{1}{7} ln ∣ v ∣

Substitute back

= \frac{1}{7} ln tan (\frac{7 x}{2})

Add a constant to the solution

= \frac{1}{7} ln tan (\frac{7 x}{2}) + C

What is the integral of csc(7x) ?
The integral of csc(7x) is 1/7 ln|tan((7x)/2)|+C