What is the integral of (10x^4+2x+1) ?

The integral of (10x^4+2x+1) is 2x^5+x^2+x+C

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integral of (10x^4+2x+1)

\int (10 x^{4} + 2 x + 1) d x

2 x^{5} + x^{2} + x + C

Solution steps

\int 10 x^{4} + 2 x + 1 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 10 x^{4} d x + \int 2 x d x + \int 1 d x

\int 10 x^{4} d x = 2 x^{5}

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

\int 1 d x = x

= 2 x^{5} + x^{2} + x

Add a constant to the solution

= 2 x^{5} + x^{2} + x + C

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What is the integral of (10x^4+2x+1) ?
The integral of (10x^4+2x+1) is 2x^5+x^2+x+C