What is the integral of 3^x-5sin(2x) ?

The integral of 3^x-5sin(2x) is (3^x)/(ln(3))+5/2 cos(2x)+C

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integral of 3^x-5sin(2x)

\int 3^{x} - 5 sin (2 x) d x

\frac{3 ^{x}}{ln ( 3 )} + \frac{5}{2} cos (2 x) + C

Solution steps

\int 3^{x} - 5 sin (2 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 3^{x} d x - \int 5 sin (2 x) d x

\int 3^{x} d x = \frac{3 ^{x}}{ln ( 3 )}

\int 5 sin (2 x) d x = - \frac{5}{2} cos (2 x)

= \frac{3 ^{x}}{ln ( 3 )} - (- \frac{5}{2} cos (2 x))

Simplify

= \frac{3 ^{x}}{ln ( 3 )} + \frac{5}{2} cos (2 x)

Add a constant to the solution

= \frac{3 ^{x}}{ln ( 3 )} + \frac{5}{2} cos (2 x) + C

n = 0 \sum \infty (n + 1)^{2}

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

y^{^{''}} - 4 y^{^{'}} + 8 y = 0

f (x) = arcsin (\frac{x}{4})

\int x^{- \frac{1}{6}} d x

What is the integral of 3^x-5sin(2x) ?
The integral of 3^x-5sin(2x) is (3^x)/(ln(3))+5/2 cos(2x)+C