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Popular >

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

Solution

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

Solution

\frac{5 x ^{6}}{6} - \frac{2 x ^{3}}{3} + C

Solution steps

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

Expand

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

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

\int 5 x^{5} d x = \frac{5 x ^{6}}{6}

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

= \frac{5 x ^{6}}{6} - \frac{2 x ^{3}}{3}

Add a constant to the solution

= \frac{5 x ^{6}}{6} - \frac{2 x ^{3}}{3} + C

Popular Examples

integral of 6x^3(-7-3x^4)^2

\int 6 x^{3} (- 7 - 3 x^{4})^{2} d x

integral of 3/(1+2y)

\int \frac{3}{1 + 2 y} d y

integral of (x+3)/(sqrt(x+2))

\int \frac{x + 3}{x + 2} d x

integral of ((12)/(1+x^2))

\int (\frac{12}{1 + x ^{2}}) d x

integral of (cos(x))/(sin^7(x))

\int \frac{cos ( x )}{sin ^{7} ( x )} d x

Frequently Asked Questions (FAQ)

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