What is the integral of 4/5+3/4 x^2-6/7 x^3 ?

The integral of 4/5+3/4 x^2-6/7 x^3 is 4/5 x+(x^3)/4-(3x^4)/(14)+C

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integral of 4/5+3/4 x^2-6/7 x^3

\int \frac{4}{5} + \frac{3}{4} x^{2} - \frac{6}{7} x^{3} d x

\frac{4}{5} x + \frac{x ^{3}}{4} - \frac{3 x ^{4}}{14} + C

Solution steps

\int \frac{4}{5} + \frac{3}{4} x^{2} - \frac{6}{7} 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{4}{5} d x + \int \frac{3}{4} x^{2} d x - \int \frac{6}{7} x^{3} d x

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

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

\int \frac{6}{7} x^{3} d x = \frac{3 x ^{4}}{14}

= \frac{4}{5} x + \frac{x ^{3}}{4} - \frac{3 x ^{4}}{14}

Add a constant to the solution

= \frac{4}{5} x + \frac{x ^{3}}{4} - \frac{3 x ^{4}}{14} + C

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What is the integral of 4/5+3/4 x^2-6/7 x^3 ?
The integral of 4/5+3/4 x^2-6/7 x^3 is 4/5 x+(x^3)/4-(3x^4)/(14)+C