What is the integral of 14x^6-12x^3+20x ?

The integral of 14x^6-12x^3+20x is 2x^7-3x^4+10x^2+C

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integral of 14x^6-12x^3+20x

\int 14 x^{6} - 12 x^{3} + 20 x d x

2 x^{7} - 3 x^{4} + 10 x^{2} + C

Solution steps

\int 14 x^{6} - 12 x^{3} + 20 x 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 14 x^{6} d x - \int 12 x^{3} d x + \int 20 x d x

\int 14 x^{6} d x = 2 x^{7}

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

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

= 2 x^{7} - 3 x^{4} + 10 x^{2}

Add a constant to the solution

= 2 x^{7} - 3 x^{4} + 10 x^{2} + C

\int (3 - x + x) d x

\int \frac{sec ^{2} ( 2 x )}{1 + 3 tan ^{2} ( 2 x )} d x

\int x + x^{4} d x

\int tan^{2} (3 x - 1) sec^{2} (3 x - 1) d x

What is the integral of 14x^6-12x^3+20x ?
The integral of 14x^6-12x^3+20x is 2x^7-3x^4+10x^2+C