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Popular Calculus >

integral of 10^{3x}

Solution

\int 1 0^{3 x} d x

Solution

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

Solution steps

\int 1 0^{3 x} d x

Simplify

1 0^{3 x} : 100 0^{x}

= \int 100 0^{x} d x

\int a^{x} d x = \frac{a ^{x}}{ln a}

= \frac{100 0 ^{x}}{ln ( 1000 )}

Simplify

ln (1000) : 3 ln (10)

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

Add a constant to the solution

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

Graph

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Frequently Asked Questions (FAQ)

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