What is the integral from 0 to 1 of 10^{3x}+10^{-3x} ?

The integral from 0 to 1 of 10^{3x}+10^{-3x} is (333333)/(1000ln(10))

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integral from 0 to 1 of 10^{3x}+10^{-3x}

\int_{0}^{1} 1 0^{3 x} + 1 0^{- 3 x} d x

\frac{333333}{1000 ln ( 10 )}

Decimal

144.76468 \dots

Solution steps

\int_{0}^{1} 1 0^{3 x} + 1 0^{- 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_{0}^{1} 1 0^{3 x} d x + \int_{0}^{1} 1 0^{- 3 x} d x

\int_{0}^{1} 1 0^{3 x} d x = \frac{333}{ln ( 10 )}

\int_{0}^{1} 1 0^{- 3 x} d x = \frac{333}{1000 ln ( 10 )}

= \frac{333}{ln ( 10 )} + \frac{333}{1000 ln ( 10 )}

Simplify

\frac{333}{ln ( 10 )} + \frac{333}{1000 ln ( 10 )} : \frac{333333}{1000 ln ( 10 )}

= \frac{333333}{1000 ln ( 10 )}

What is the integral from 0 to 1 of 10^{3x}+10^{-3x} ?
The integral from 0 to 1 of 10^{3x}+10^{-3x} is (333333)/(1000ln(10))