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

= \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

: \int \frac{1}{v} d v

= \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

\int_{0}^{\frac{π}{2}} 4 cos (\frac{x}{2}) d x

\frac{d}{d y} (\frac{y ^{3}}{9} + \frac{3}{4 y})

\frac{\partial}{\partial y} (2 x^{2} yz)

v \to 4 lim (\frac{v ^{2} - 6 v + 8}{2 v ^{2} - 8 v})

\frac{\partial}{\partial t} (r cos (t))

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