What is the integral of-x^{7.2}+4x^4+5sqrt(x)-6 ?

The integral of-x^{7.2}+4x^4+5sqrt(x)-6 is -0.12195…x^{8.2}+0.8x^5+3.33333…x^{3/2}-6x+C

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integral of-x^{7.2}+4x^4+5sqrt(x)-6

\int - x^{7.2} + 4 x^{4} + 5 x - 6 d x

- 0.12195 \dots x^{8.2} + 0.8 x^{5} + 3.33333 \dots x^{\frac{3}{2}} - 6 x + C

Solution steps

\int - x^{7.2} + 4 x^{4} + 5 x - 6 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 x^{7.2} d x + \int 4 x^{4} d x + \int 5 x d x - \int 6 d x

\int x^{7.2} d x = 0.12195 \dots x^{8.2}

\int 4 x^{4} d x = \frac{4 x ^{5}}{5}

\int 5 x d x = \frac{10}{3} x^{\frac{3}{2}}

\int 6 d x = 6 x

= - 0.12195 \dots x^{8.2} + \frac{4 x ^{5}}{5} + \frac{10}{3} x^{\frac{3}{2}} - 6 x

Simplify

= - 0.12195 \dots x^{8.2} + 0.8 x^{5} + 3.33333 \dots x^{\frac{3}{2}} - 6 x

Add a constant to the solution

= - 0.12195 \dots x^{8.2} + 0.8 x^{5} + 3.33333 \dots x^{\frac{3}{2}} - 6 x + C

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What is the integral of-x^{7.2}+4x^4+5sqrt(x)-6 ?
The integral of-x^{7.2}+4x^4+5sqrt(x)-6 is -0.12195…x^{8.2}+0.8x^5+3.33333…x^{3/2}-6x+C