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

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

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

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

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

Solution steps

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

Expand

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

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

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

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

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

Add a constant to the solution

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

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