What is the integral from 0 to 1 of (5x-5^x) ?

The integral from 0 to 1 of (5x-5^x) is 5/2-4/(ln(5))

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integral from 0 to 1 of (5x-5^x)

\int_{0}^{1} (5 x - 5^{x}) d x

\frac{5}{2} - \frac{4}{ln ( 5 )}

Decimal

0.01466 \dots

Solution steps

\int_{0}^{1} 5 x - 5^{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} 5 x d x - \int_{0}^{1} 5^{x} d x

\int_{0}^{1} 5 x d x = \frac{5}{2}

\int_{0}^{1} 5^{x} d x = \frac{4}{ln ( 5 )}

= \frac{5}{2} - \frac{4}{ln ( 5 )}

\int x sin (11 - x) d x

\int \frac{1}{πn} sin (nπ x) d x

f (x) = x^{2} (3 + x)^{- 5}

\frac{d}{d t} (e^{t} (cos (t) - sin (t)))

f (x) = ln (25 sin (2) (x))

What is the integral from 0 to 1 of (5x-5^x) ?
The integral from 0 to 1 of (5x-5^x) is 5/2-4/(ln(5))