What is the integral of (2^x-4sin(x)) ?

The integral of (2^x-4sin(x)) is (2^x)/(ln(2))+4cos(x)+C

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integral of (2^x-4sin(x))

\int (2^{x} - 4 sin (x)) d x

\frac{2 ^{x}}{ln ( 2 )} + 4 cos (x) + C

Solution steps

\int 2^{x} - 4 sin (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 2^{x} d x - \int 4 sin (x) d x

\int 2^{x} d x = \frac{2 ^{x}}{ln ( 2 )}

\int 4 sin (x) d x = - 4 cos (x)

= \frac{2 ^{x}}{ln ( 2 )} - (- 4 cos (x))

Simplify

= \frac{2 ^{x}}{ln ( 2 )} + 4 cos (x)

Add a constant to the solution

= \frac{2 ^{x}}{ln ( 2 )} + 4 cos (x) + C

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What is the integral of (2^x-4sin(x)) ?
The integral of (2^x-4sin(x)) is (2^x)/(ln(2))+4cos(x)+C