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

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

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

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

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

Solution steps

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

Expand

(4 x^{3} - 2) x^{2} : 4 x^{5} - 2 x^{2}

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

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

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

= \frac{2 x ^{6}}{3} - \frac{2 x ^{3}}{3}

Add a constant to the solution

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

n = 1 \sum \infty \frac{n !}{5 ^{n}}

f (x) = \frac{1}{x ^{16}}

\int \frac{x ^{3}}{3} d x

t e^{t}

\frac{d ^{7}}{d x ^{7}} ((2 x + 5)^{7})

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