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Popular >

integral of x^3-2x+2

Solution

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

Solution

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

Solution steps

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

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

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

\int 2 d x = 2 x

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

Add a constant to the solution

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

Popular Examples

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

\int \frac{1 + x ^{2}}{x} d x

integral of log_{4}(3x+1)

\int lo g_{4} (3 x + 1) d x

3y^{''}+2y^'-y=0

3 y^{^{''}} + 2 y^{^{'}} - y = 0

integral of x(2x+1)e^{4x^3+3x^2-4}

\int x (2 x + 1) e^{4 x^{3} + 3 x^{2} - 4} d x

y^{^{'}} + y^{2} = 1

Frequently Asked Questions (FAQ)

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