What is the integral of (4x^5+5x^3+11) ?

The integral of (4x^5+5x^3+11) is (2x^6)/3+(5x^4)/4+11x+C

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integral of (4x^5+5x^3+11)

\int (4 x^{5} + 5 x^{3} + 11) d x

\frac{2 x ^{6}}{3} + \frac{5 x ^{4}}{4} + 11 x + C

Solution steps

\int 4 x^{5} + 5 x^{3} + 11 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 4 x^{5} d x + \int 5 x^{3} d x + \int 11 d x

\int 4 x^{5} d x = \frac{2 x ^{6}}{3}

\int 5 x^{3} d x = \frac{5 x ^{4}}{4}

\int 11 d x = 11 x

= \frac{2 x ^{6}}{3} + \frac{5 x ^{4}}{4} + 11 x

Add a constant to the solution

= \frac{2 x ^{6}}{3} + \frac{5 x ^{4}}{4} + 11 x + C

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What is the integral of (4x^5+5x^3+11) ?
The integral of (4x^5+5x^3+11) is (2x^6)/3+(5x^4)/4+11x+C