What is the integral of 5m(12m^3-10m) ?

The integral of 5m(12m^3-10m) is 12m^5-(50m^3)/3+C

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integral of 5m(12m^3-10m)

\int 5 m (12 m^{3} - 10 m) d m

12 m^{5} - \frac{50 m ^{3}}{3} + C

Solution steps

\int 5 m (12 m^{3} - 10 m) d m

Take the constant out:

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

= 5 \cdot \int m (12 m^{3} - 10 m) d m

Expand

m (12 m^{3} - 10 m) : 12 m^{4} - 10 m^{2}

= 5 \cdot \int 12 m^{4} - 10 m^{2} d m

Apply the Sum Rule:

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

= 5 (\int 12 m^{4} d m - \int 10 m^{2} d m)

\int 12 m^{4} d m = \frac{12 m ^{5}}{5}

\int 10 m^{2} d m = \frac{10 m ^{3}}{3}

= 5 (\frac{12 m ^{5}}{5} - \frac{10 m ^{3}}{3})

Simplify

5 (\frac{12 m ^{5}}{5} - \frac{10 m ^{3}}{3}) : 12 m^{5} - \frac{50 m ^{3}}{3}

= 12 m^{5} - \frac{50 m ^{3}}{3}

Add a constant to the solution

= 12 m^{5} - \frac{50 m ^{3}}{3} + C

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What is the integral of 5m(12m^3-10m) ?
The integral of 5m(12m^3-10m) is 12m^5-(50m^3)/3+C