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Popular Calculus >

integral of 3x^2-5x

Solution

\int 3 x^{2} - 5 x d x

Solution

x^{3} - \frac{5 x ^{2}}{2} + C

Solution steps

\int 3 x^{2} - 5 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 3 x^{2} d x - \int 5 x d x

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

\int 5 x d x = \frac{5 x ^{2}}{2}

= x^{3} - \frac{5 x ^{2}}{2}

Add a constant to the solution

= x^{3} - \frac{5 x ^{2}}{2} + C

Graph

Popular Examples

integral of (x+5)/(x^2-2x-3)

\int \frac{x + 5}{x ^{2} - 2 x - 3} d x

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

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

integral of (x+1)^6

\int (x + 1)^{6} d x

integral of (4+5x)^5

\int (4 + 5 x)^{5} d x

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

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

Frequently Asked Questions (FAQ)

What is the integral of 3x^2-5x ?
The integral of 3x^2-5x is x^3-(5x^2)/2+C