What is the integral of xcsc(6x^2) ?

The integral of xcsc(6x^2) is 1/12 ln|tan(3x^2)|+C

Popular >

integral of xcsc(6x^2)

\int x csc (6 x^{2}) d x

\frac{1}{12} ln tan (3 x^{2}) + C

Solution steps

\int x csc (6 x^{2}) d x

Apply u-substitution

: \int \frac{csc ( u )}{12} d u

= \int \frac{csc ( u )}{12} d u

Take the constant out:

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

= \frac{1}{12} \cdot \int csc (u) d u

Apply u-substitution

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

= \frac{1}{12} \cdot \int \frac{1}{v} d v

Use the common integral:

\int \frac{1}{v} d v = ln (∣ v ∣)

= \frac{1}{12} ln ∣ v ∣

Substitute back

= \frac{1}{12} ln tan (\frac{6 x ^{2}}{2})

Simplify

\frac{1}{12} ln tan (\frac{6 x ^{2}}{2}) : \frac{1}{12} ln tan (3 x^{2})

= \frac{1}{12} ln tan (3 x^{2})

Add a constant to the solution

= \frac{1}{12} ln tan (3 x^{2}) + C

\frac{d y}{d t} = \frac{t e ^{t}}{y 5 + y ^{2}}

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

\frac{d}{d x} (e^{x, x})

\frac{( s + 1 )}{( s ^{2} + s + 10 )}

\int_{4}^{8} 1 - \frac{4}{x} d x

What is the integral of xcsc(6x^2) ?
The integral of xcsc(6x^2) is 1/12 ln|tan(3x^2)|+C