What is the integral of (3cos(x)-3^x) ?

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

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integral of (3cos(x)-3^x)

\int (3 cos (x) - 3^{x}) d x

3 sin (x) - \frac{3 ^{x}}{ln ( 3 )} + C

Solution steps

\int 3 cos (x) - 3^{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 cos (x) d x - \int 3^{x} d x

\int 3 cos (x) d x = 3 sin (x)

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

= 3 sin (x) - \frac{3 ^{x}}{ln ( 3 )}

Add a constant to the solution

= 3 sin (x) - \frac{3 ^{x}}{ln ( 3 )} + C

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\int \frac{( x ^{3} + 4 x + 3 )}{x ^{4} + 5 x ^{2} + 4} d x

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