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Popular >

integral of 1+x-3x^2

Solution

\int 1 + x - 3 x^{2} d x

Solution

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

Solution steps

\int 1 + x - 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 1 d x + \int x d x - \int 3 x^{2} d x

\int 1 d x = x

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

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

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

Add a constant to the solution

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

Popular Examples

integral of t^1

\int t^{1} d t

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\int \frac{x}{5 x + 1} d x

integral of (2x)/(1-3x^2)

\int \frac{2 x}{1 - 3 x ^{2}} d x

integral of (5x^2+3)cos(x)

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

integral of (x-2)e^{-x^2+4x}

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

Frequently Asked Questions (FAQ)

What is the integral of 1+x-3x^2 ?
The integral of 1+x-3x^2 is x+(x^2)/2-x^3+C