What is the integral of (13-6x+21x^6) ?

The integral of (13-6x+21x^6) is 13x-3x^2+3x^7+C

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integral of (13-6x+21x^6)

\int (13 - 6 x + 21 x^{6}) d x

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

Solution steps

\int 13 - 6 x + 21 x^{6} 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 13 d x - \int 6 x d x + \int 21 x^{6} d x

\int 13 d x = 13 x

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

\int 21 x^{6} d x = 3 x^{7}

= 13 x - 3 x^{2} + 3 x^{7}

Add a constant to the solution

= 13 x - 3 x^{2} + 3 x^{7} + C

\frac{d}{d x} (\frac{cos ( 2 x )}{sin ( x )})

\int_{1}^{2} \frac{x}{x ^{2} + 4 x + 20} d x

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\frac{d}{d x} (x^{2} \cdot x)

What is the integral of (13-6x+21x^6) ?
The integral of (13-6x+21x^6) is 13x-3x^2+3x^7+C