What is the integral of u^{1.1}(1/(3u)-1) ?

The integral of u^{1.1}(1/(3u)-1) is 0.30303…u^{1.1}-0.47619…u^{2.1}+C

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integral of u^{1.1}(1/(3u)-1)

\int u^{1.1} (\frac{1}{3 u} - 1) d u

0.30303 \dots u^{1.1} - 0.47619 \dots u^{2.1} + C

Solution steps

\int u^{1.1} (\frac{1}{3 u} - 1) d u

Expand

u^{1.1} (\frac{1}{3 u} - 1) : \frac{u ^{0.1}}{3} - u^{1.1}

= \int \frac{u ^{0.1}}{3} - u^{1.1} d u

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int \frac{u ^{0.1}}{3} d u - \int u^{1.1} d u

\int \frac{u ^{0.1}}{3} d u = 0.30303 \dots u^{1.1}

\int u^{1.1} d u = 0.47619 \dots u^{2.1}

= 0.30303 \dots u^{1.1} - 0.47619 \dots u^{2.1}

Add a constant to the solution

= 0.30303 \dots u^{1.1} - 0.47619 \dots u^{2.1} + C

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What is the integral of u^{1.1}(1/(3u)-1) ?
The integral of u^{1.1}(1/(3u)-1) is 0.30303…u^{1.1}-0.47619…u^{2.1}+C