What is the integral of (5x^6+8x^3+11) ?

The integral of (5x^6+8x^3+11) is (5x^7)/7+2x^4+11x+C

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integral of (5x^6+8x^3+11)

\int (5 x^{6} + 8 x^{3} + 11) d x

\frac{5 x ^{7}}{7} + 2 x^{4} + 11 x + C

Solution steps

\int 5 x^{6} + 8 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 5 x^{6} d x + \int 8 x^{3} d x + \int 11 d x

\int 5 x^{6} d x = \frac{5 x ^{7}}{7}

\int 8 x^{3} d x = 2 x^{4}

\int 11 d x = 11 x

= \frac{5 x ^{7}}{7} + 2 x^{4} + 11 x

Add a constant to the solution

= \frac{5 x ^{7}}{7} + 2 x^{4} + 11 x + C

What is the integral of (5x^6+8x^3+11) ?
The integral of (5x^6+8x^3+11) is (5x^7)/7+2x^4+11x+C