What is the integral of (25x^4+82x) ?

The integral of (25x^4+82x) is 5x^5+41x^2+C

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integral of (25x^4+82x)

\int (25 x^{4} + 82 x) d x

5 x^{5} + 41 x^{2} + C

Solution steps

\int 25 x^{4} + 82 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 25 x^{4} d x + \int 82 x d x

\int 25 x^{4} d x = 5 x^{5}

\int 82 x d x = 41 x^{2}

= 5 x^{5} + 41 x^{2}

Add a constant to the solution

= 5 x^{5} + 41 x^{2} + C

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What is the integral of (25x^4+82x) ?
The integral of (25x^4+82x) is 5x^5+41x^2+C