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Popular >

integral of x^3-3x^2-x+3

Solution

\int x^{3} - 3 x^{2} - x + 3 d x

Solution

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

Solution steps

\int x^{3} - 3 x^{2} - 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 x^{3} d x - \int 3 x^{2} d x - \int x d x + \int 3 d x

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

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

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

\int 3 d x = 3 x

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

Add a constant to the solution

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

Popular Examples

(\partial)/(\partial y)(3)

\frac{\partial}{\partial y} (3)

integral of sin^2(6x)

\int sin^{2} (6 x) d x

(\partial)/(\partial y)(ycos(yz))

\frac{\partial}{\partial y} (y cos (yz))

derivative of x^3+3x^2-2

\frac{d}{d x} (x^{3} + 3 x^{2} - 2)

y^{^{'}} = (1 + x) (1 + y)

Frequently Asked Questions (FAQ)

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