What is the integral of 56x^6(1-x) ?

The integral of 56x^6(1-x) is 56((x^7)/7-(x^8)/8)+C

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integral of 56x^6(1-x)

\int 56 x^{6} (1 - x) d x

56 (\frac{x ^{7}}{7} - \frac{x ^{8}}{8}) + C

Solution steps

\int 56 x^{6} (1 - x) d x

Take the constant out:

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

= 56 \cdot \int x^{6} (1 - x) d x

Expand

x^{6} (1 - x) : x^{6} - x^{7}

= 56 \cdot \int x^{6} - x^{7} 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

= 56 (\int x^{6} d x - \int x^{7} d x)

\int x^{6} d x = \frac{x ^{7}}{7}

\int x^{7} d x = \frac{x ^{8}}{8}

= 56 (\frac{x ^{7}}{7} - \frac{x ^{8}}{8})

Add a constant to the solution

= 56 (\frac{x ^{7}}{7} - \frac{x ^{8}}{8}) + C

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What is the integral of 56x^6(1-x) ?
The integral of 56x^6(1-x) is 56((x^7)/7-(x^8)/8)+C