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

The integral from 1 to e^6 of (6ln(x))/x is 108

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integral from 1 to e^6 of (6ln(x))/x

\int_{1}^{e^{6}} \frac{6 ln ( x )}{x} d x

108

Solution steps

\int_{1}^{e^{6}} \frac{6 ln ( x )}{x} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 6 \cdot \int_{1}^{e^{6}} \frac{ln ( x )}{x} d x

Apply u-substitution

= 6 \cdot \int_{0}^{6} u d u

Apply the Power Rule

= 6 [\frac{u ^{2}}{2}]_{0}^{6}

Compute the boundaries:

18

= 6 \cdot 18

Simplify

= 108

\int_{0}^{\frac{π}{6}} tan^{2} (x) d x

\int_{2}^{3} \frac{x ^{2} + 1}{x} d x

\int_{\frac{π}{8}}^{\frac{π}{6}} tan^{2} (2 x) d x

\int_{0}^{1} π (7 x^{2})^{2} d x

\int_{1}^{2} x^{\frac{3}{5}} d x

What is the integral from 1 to e^6 of (6ln(x))/x ?
The integral from 1 to e^6 of (6ln(x))/x is 108