What is the integral of (csc^2(x)-a^x) ?

The integral of (csc^2(x)-a^x) is -cot(x)-(a^x)/(ln(a))+C

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integral of (csc^2(x)-a^x)

\int (csc^{2} (x) - a^{x}) d x

- cot (x) - \frac{a ^{x}}{ln ( a )} + C

Solution steps

\int csc^{2} (x) - a^{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 csc^{2} (x) d x - \int a^{x} d x

\int csc^{2} (x) d x = - cot (x)

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

= - cot (x) - \frac{a ^{x}}{ln ( a )}

Add a constant to the solution

= - cot (x) - \frac{a ^{x}}{ln ( a )} + C

x \to \infty lim (0^{- x})

y^{^{''}} - 2 y^{^{'}} + 1 y = 0, y (0) = 5, y^{^{'}} (0) = 4

ln (x - 9)

\frac{\partial}{\partial x} ((x + 1)^{2} (x^{2} + 2 x))

f (x) = \frac{x ^{3} - 1 x ^{2} + 2}{x ^{2}}

What is the integral of (csc^2(x)-a^x) ?
The integral of (csc^2(x)-a^x) is -cot(x)-(a^x)/(ln(a))+C