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Popular >

integral of x^3+3x-2

Solution

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

Solution

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

Solution steps

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

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

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

\int 2 d x = 2 x

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

Add a constant to the solution

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

Popular Examples

d/(dt)(1/3 t^3+1/2 t^2)

\frac{d}{d t} (\frac{1}{3} t^{3} + \frac{1}{2} t^{2})

derivative of e^{-8x^2}

\frac{d}{d x} (e^{- 8 x^{2}})

(\partial)/(\partial y)(e^{(x+y)}-1)

\frac{\partial}{\partial y} (e^{(x + y)} - 1)

(\partial)/(\partial z)(3ycos(pix)+2xz)

\frac{\partial}{\partial z} (3 y cos (π x) + 2 x z)

derivative of 3/(3x-5)

\frac{d}{d x} (\frac{3}{3 x - 5})

Frequently Asked Questions (FAQ)

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