What is the integral of x^2(20x^7-7x^4+6) ?

The integral of x^2(20x^7-7x^4+6) is 2x^{10}-x^7+2x^3+C

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integral of x^2(20x^7-7x^4+6)

\int x^{2} (20 x^{7} - 7 x^{4} + 6) d x

2 x^{10} - x^{7} + 2 x^{3} + C

Solution steps

\int x^{2} (20 x^{7} - 7 x^{4} + 6) d x

Expand

x^{2} (20 x^{7} - 7 x^{4} + 6) : 20 x^{9} - 7 x^{6} + 6 x^{2}

= \int 20 x^{9} - 7 x^{6} + 6 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

= \int 20 x^{9} d x - \int 7 x^{6} d x + \int 6 x^{2} d x

\int 20 x^{9} d x = 2 x^{10}

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

\int 6 x^{2} d x = 2 x^{3}

= 2 x^{10} - x^{7} + 2 x^{3}

Add a constant to the solution

= 2 x^{10} - x^{7} + 2 x^{3} + C

sin (x^{5})

x = 7 y^{2}, x = 4 + 3 y^{2}

\int x ln (x) - x d x

\int \frac{1}{2 x ^{2} - 5 x + 3} d x

\int_{0}^{1} x^{\frac{1}{3}} - x^{3} d x

What is the integral of x^2(20x^7-7x^4+6) ?
The integral of x^2(20x^7-7x^4+6) is 2x^{10}-x^7+2x^3+C