What is the integral of 2^x+8sinh(x) ?

The integral of 2^x+8sinh(x) is (2^x)/(ln(2))+8cosh(x)+C

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integral of 2^x+8sinh(x)

\int 2^{x} + 8 sinh (x) d x

\frac{2 ^{x}}{ln ( 2 )} + 8 cosh (x) + C

Solution steps

\int 2^{x} + 8 sinh (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 8 sinh (x) d x

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

\int 8 sinh (x) d x = 8 cosh (x)

= \frac{2 ^{x}}{ln ( 2 )} + 8 cosh (x)

Add a constant to the solution

= \frac{2 ^{x}}{ln ( 2 )} + 8 cosh (x) + C

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What is the integral of 2^x+8sinh(x) ?
The integral of 2^x+8sinh(x) is (2^x)/(ln(2))+8cosh(x)+C