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Popular >

integral of 2x^3-3x

Solution

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

Solution

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

Solution steps

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

\int 2 x^{3} d x = \frac{x ^{4}}{2}

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

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

Add a constant to the solution

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

Popular Examples

integral of 3e^{0.5x}

\int 3 e^{0.5 x} d x

integral of 1/(x(x+b))

\int \frac{1}{x ( x + b )} d x

integral of 5^xsin(x)

\int 5^{x} sin (x) d x

integral of (x^3-8x+1)/(8x^4)

\int \frac{x ^{3} - 8 x + 1}{8 x ^{4}} d x

integral of x/(b-a)

\int \frac{x}{b - a} d x

Frequently Asked Questions (FAQ)

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