What is the integral of 2x^2(x^3+5) ?

The integral of 2x^2(x^3+5) is 2((x^6)/6+(5x^3)/3)+C

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integral of 2x^2(x^3+5)

\int 2 x^{2} (x^{3} + 5) d x

2 (\frac{x ^{6}}{6} + \frac{5 x ^{3}}{3}) + C

Solution steps

\int 2 x^{2} (x^{3} + 5) d x

Take the constant out:

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

= 2 \cdot \int x^{2} (x^{3} + 5) d x

Expand

x^{2} (x^{3} + 5) : x^{5} + 5 x^{2}

= 2 \cdot \int x^{5} + 5 x^{2} 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

= 2 (\int x^{5} d x + \int 5 x^{2} d x)

\int x^{5} d x = \frac{x ^{6}}{6}

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

= 2 (\frac{x ^{6}}{6} + \frac{5 x ^{3}}{3})

Add a constant to the solution

= 2 (\frac{x ^{6}}{6} + \frac{5 x ^{3}}{3}) + C

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What is the integral of 2x^2(x^3+5) ?
The integral of 2x^2(x^3+5) is 2((x^6)/6+(5x^3)/3)+C