Primitive of Reciprocal of Sine of a x

Theorem

Logarithm of Cosecant minus Cotangent Form

$\ds \int \frac {\d x} {\sin a x} = \frac 1 a \ln \size {\csc a x - \cot a x} + C$

Logarithm of Tangent Form

$\ds \int \frac {\d x} {\sin a x} = \frac 1 a \ln \size {\tan \frac {a x} 2} + C$

Also see

• Primitive of $\dfrac 1 {\cos a x}$

• Primitive of $\dfrac 1 {\tan a x}$

• Primitive of $\dfrac 1 {\cot a x}$

• Primitive of $\dfrac 1 {\sec a x}$

• Primitive of $\dfrac 1 {\csc a x}$