What is the integral of (10^{3x}-2^x) ?

The integral of (10^{3x}-2^x) is (1000^x)/(3ln(10))-(2^x)/(ln(2))+C

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integral of (10^{3x}-2^x)

\int (1 0^{3 x} - 2^{x}) d x

\frac{100 0 ^{x}}{3 ln ( 10 )} - \frac{2 ^{x}}{ln ( 2 )} + C

Solution steps

\int 1 0^{3 x} - 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 1 0^{3 x} d x - \int 2^{x} d x

\int 1 0^{3 x} d x = \frac{100 0 ^{x}}{3 ln ( 10 )}

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

= \frac{100 0 ^{x}}{3 ln ( 10 )} - \frac{2 ^{x}}{ln ( 2 )}

Add a constant to the solution

= \frac{100 0 ^{x}}{3 ln ( 10 )} - \frac{2 ^{x}}{ln ( 2 )} + C

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What is the integral of (10^{3x}-2^x) ?
The integral of (10^{3x}-2^x) is (1000^x)/(3ln(10))-(2^x)/(ln(2))+C