What is the integral of 3^{csc(x)}csc(x)cot(x) ?

The integral of 3^{csc(x)}csc(x)cot(x) is -(3^{csc(x)})/(ln(3))+C

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integral of 3^{csc(x)}csc(x)cot(x)

\int 3^{c s c (x)} csc (x) cot (x) d x

- \frac{3 ^{c s c (x)}}{ln ( 3 )} + C

Solution steps

\int 3^{c s c (x)} csc (x) cot (x) d x

Apply u-substitution

: \int - 3^{u} d u

= \int - 3^{u} d u

Take the constant out:

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

= - \int 3^{u} d u

\int a^{x} d x = \frac{a ^{x}}{ln a}

= - \frac{3 ^{u}}{ln ( 3 )}

Substitute back

u = csc (x)

= - \frac{3 ^{c s c (x)}}{ln ( 3 )}

Add a constant to the solution

= - \frac{3 ^{c s c (x)}}{ln ( 3 )} + C

9 sin (2 x)

\int 3 cos^{3} (x) d x

\frac{d}{d x} (\frac{4 x ^{2} + 8 x + 6}{x})

\int_{0}^{1} x 4 + 9 x^{2} d x

\int e^{2 x} \cdot sin (e^{x}) d x

What is the integral of 3^{csc(x)}csc(x)cot(x) ?
The integral of 3^{csc(x)}csc(x)cot(x) is -(3^{csc(x)})/(ln(3))+C