What is the integral of 5x^4+3x^2+1 ?

The integral of 5x^4+3x^2+1 is x^5+x^3+x+C

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integral of 5x^4+3x^2+1

\int 5 x^{4} + 3 x^{2} + 1 d x

x^{5} + x^{3} + x + C

Solution steps

\int 5 x^{4} + 3 x^{2} + 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 5 x^{4} d x + \int 3 x^{2} d x + \int 1 d x

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

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

\int 1 d x = x

= x^{5} + x^{3} + x

Add a constant to the solution

= x^{5} + x^{3} + x + C

What is the integral of 5x^4+3x^2+1 ?
The integral of 5x^4+3x^2+1 is x^5+x^3+x+C