What is the integral of (6-6csc(x)cot(x)-6^x) ?

The integral of (6-6csc(x)cot(x)-6^x) is 6x+6csc(x)-(6^x)/(ln(6))+C

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integral of (6-6csc(x)cot(x)-6^x)

\int (6 - 6 csc (x) cot (x) - 6^{x}) d x

6 x + 6 csc (x) - \frac{6 ^{x}}{ln ( 6 )} + C

Solution steps

\int 6 - 6 csc (x) cot (x) - 6^{x} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 6 d x - \int 6 csc (x) cot (x) d x - \int 6^{x} d x

\int 6 d x = 6 x

\int 6 csc (x) cot (x) d x = - 6 csc (x)

\int 6^{x} d x = \frac{6 ^{x}}{ln ( 6 )}

= 6 x - (- 6 csc (x)) - \frac{6 ^{x}}{ln ( 6 )}

Simplify

= 6 x + 6 csc (x) - \frac{6 ^{x}}{ln ( 6 )}

Add a constant to the solution

= 6 x + 6 csc (x) - \frac{6 ^{x}}{ln ( 6 )} + C

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What is the integral of (6-6csc(x)cot(x)-6^x) ?
The integral of (6-6csc(x)cot(x)-6^x) is 6x+6csc(x)-(6^x)/(ln(6))+C