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

The integral of (3/4 x-2/5)^2 is (3x^3)/(16)-(3x^2)/(10)+4/25 x+C

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

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

\frac{3 x ^{3}}{16} - \frac{3 x ^{2}}{10} + \frac{4}{25} x + C

Solution steps

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

Expand

(\frac{3}{4} x - \frac{2}{5})^{2} : \frac{9 x ^{2}}{16} - \frac{3 x}{5} + \frac{4}{25}

= \int \frac{9 x ^{2}}{16} - \frac{3 x}{5} + \frac{4}{25} 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{9 x ^{2}}{16} d x - \int \frac{3 x}{5} d x + \int \frac{4}{25} d x

\int \frac{9 x ^{2}}{16} d x = \frac{3 x ^{3}}{16}

\int \frac{3 x}{5} d x = \frac{3 x ^{2}}{10}

\int \frac{4}{25} d x = \frac{4}{25} x

= \frac{3 x ^{3}}{16} - \frac{3 x ^{2}}{10} + \frac{4}{25} x

Add a constant to the solution

= \frac{3 x ^{3}}{16} - \frac{3 x ^{2}}{10} + \frac{4}{25} x + C

What is the integral of (3/4 x-2/5)^2 ?
The integral of (3/4 x-2/5)^2 is (3x^3)/(16)-(3x^2)/(10)+4/25 x+C