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

The integral of (4x^3+(x^2)/3-4/5 x+5/6) is x^4+(x^3)/9-(2x^2)/5+5/6 x+C

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integral of (4x^3+(x^2)/3-4/5 x+5/6)

\int (4 x^{3} + \frac{x ^{2}}{3} - \frac{4}{5} x + \frac{5}{6}) d x

x^{4} + \frac{x ^{3}}{9} - \frac{2 x ^{2}}{5} + \frac{5}{6} x + C

Solution steps

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

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

\int \frac{x ^{2}}{3} d x = \frac{x ^{3}}{9}

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

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

= x^{4} + \frac{x ^{3}}{9} - \frac{2 x ^{2}}{5} + \frac{5}{6} x

Add a constant to the solution

= x^{4} + \frac{x ^{3}}{9} - \frac{2 x ^{2}}{5} + \frac{5}{6} x + C

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What is the integral of (4x^3+(x^2)/3-4/5 x+5/6) ?
The integral of (4x^3+(x^2)/3-4/5 x+5/6) is x^4+(x^3)/9-(2x^2)/5+5/6 x+C