What is the integral of (8x^9-3x^6+12x^3) ?

The integral of (8x^9-3x^6+12x^3) is (4x^{10})/5-(3x^7)/7+3x^4+C

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integral of (8x^9-3x^6+12x^3)

\int (8 x^{9} - 3 x^{6} + 12 x^{3}) d x

\frac{4 x ^{10}}{5} - \frac{3 x ^{7}}{7} + 3 x^{4} + C

Solution steps

\int 8 x^{9} - 3 x^{6} + 12 x^{3} 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 8 x^{9} d x - \int 3 x^{6} d x + \int 12 x^{3} d x

\int 8 x^{9} d x = \frac{4 x ^{10}}{5}

\int 3 x^{6} d x = \frac{3 x ^{7}}{7}

\int 12 x^{3} d x = 3 x^{4}

= \frac{4 x ^{10}}{5} - \frac{3 x ^{7}}{7} + 3 x^{4}

Add a constant to the solution

= \frac{4 x ^{10}}{5} - \frac{3 x ^{7}}{7} + 3 x^{4} + C

What is the integral of (8x^9-3x^6+12x^3) ?
The integral of (8x^9-3x^6+12x^3) is (4x^{10})/5-(3x^7)/7+3x^4+C