What is the integral of (3x^2)/5+(7x^3)/8 ?

The integral of (3x^2)/5+(7x^3)/8 is (x^3)/5+(7x^4)/(32)+C

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integral of (3x^2)/5+(7x^3)/8

\int \frac{3 x ^{2}}{5} + \frac{7 x ^{3}}{8} d x

\frac{x ^{3}}{5} + \frac{7 x ^{4}}{32} + C

Solution steps

\int \frac{3 x ^{2}}{5} + \frac{7 x ^{3}}{8} 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 x ^{2}}{5} d x + \int \frac{7 x ^{3}}{8} d x

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

\int \frac{7 x ^{3}}{8} d x = \frac{7 x ^{4}}{32}

= \frac{x ^{3}}{5} + \frac{7 x ^{4}}{32}

Add a constant to the solution

= \frac{x ^{3}}{5} + \frac{7 x ^{4}}{32} + C

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What is the integral of (3x^2)/5+(7x^3)/8 ?
The integral of (3x^2)/5+(7x^3)/8 is (x^3)/5+(7x^4)/(32)+C