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

The integral of 3/4+4/5 x^2-5/6 x^3 is 3/4 x+(4x^3)/(15)-(5x^4)/(24)+C

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

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

\frac{3}{4} x + \frac{4 x ^{3}}{15} - \frac{5 x ^{4}}{24} + C

Solution steps

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

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

\int \frac{4}{5} x^{2} d x = \frac{4 x ^{3}}{15}

\int \frac{5}{6} x^{3} d x = \frac{5 x ^{4}}{24}

= \frac{3}{4} x + \frac{4 x ^{3}}{15} - \frac{5 x ^{4}}{24}

Add a constant to the solution

= \frac{3}{4} x + \frac{4 x ^{3}}{15} - \frac{5 x ^{4}}{24} + C

What is the integral of 3/4+4/5 x^2-5/6 x^3 ?
The integral of 3/4+4/5 x^2-5/6 x^3 is 3/4 x+(4x^3)/(15)-(5x^4)/(24)+C