What is the integral from 1 to 6 of (5^{ln(x)})/x ?

The integral from 1 to 6 of (5^{ln(x)})/x is (5^{ln(6)}-1)/(ln(5))

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integral from 1 to 6 of (5^{ln(x)})/x

\int_{1}^{6} \frac{5 ^{l n (x)}}{x} d x

\frac{5 ^{l n (6)} - 1}{ln ( 5 )}

Decimal Notation

10.48860 \dots

Solution steps

\int_{1}^{6} \frac{5 ^{l n (x)}}{x} d x

Apply u-substitution

: \int_{0}^{l n (6)} 5^{u} d u

= \int_{0}^{l n (6)} 5^{u} d u

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

= [\frac{5 ^{u}}{ln ( 5 )}]_{0}^{l n (6)}

Compute the boundaries:

\frac{5 ^{l n (6)} - 1}{ln ( 5 )}

= \frac{5 ^{l n (6)} - 1}{ln ( 5 )}

n = 0 \sum \infty 3 (\frac{3}{2})^{n}

\int (\frac{1}{x} - \frac{6}{x ^{2} + 1}) d x

\int_{0}^{16} x - \frac{1}{4} x d x

\frac{d}{d x} (\frac{4 x + 5}{8})

y = \frac{3}{x}, (5, \frac{3}{5})

What is the integral from 1 to 6 of (5^{ln(x)})/x ?
The integral from 1 to 6 of (5^{ln(x)})/x is (5^{ln(6)}-1)/(ln(5))