What is the integral of (2x^5+2x^2+5) ?

The integral of (2x^5+2x^2+5) is (x^6)/3+(2x^3)/3+5x+C

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integral of (2x^5+2x^2+5)

\int (2 x^{5} + 2 x^{2} + 5) d x

\frac{x ^{6}}{3} + \frac{2 x ^{3}}{3} + 5 x + C

Solution steps

\int 2 x^{5} + 2 x^{2} + 5 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 2 x^{5} d x + \int 2 x^{2} d x + \int 5 d x

\int 2 x^{5} d x = \frac{x ^{6}}{3}

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

\int 5 d x = 5 x

= \frac{x ^{6}}{3} + \frac{2 x ^{3}}{3} + 5 x

Add a constant to the solution

= \frac{x ^{6}}{3} + \frac{2 x ^{3}}{3} + 5 x + C

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\int cos (x) - 2 sin (x) d x

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What is the integral of (2x^5+2x^2+5) ?
The integral of (2x^5+2x^2+5) is (x^6)/3+(2x^3)/3+5x+C