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Popular >

integral of x^2+5x-3

Solution

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

Solution

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

Solution steps

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

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

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

\int 3 d x = 3 x

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

Add a constant to the solution

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

Graph

Popular Examples

integral of (3x)/(sqrt(4x+7))

\int \frac{3 x}{4 x + 7} d x

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

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

integral of (x^3+3x)^8(x^2+1)

\int (x^{3} + 3 x)^{8} (x^{2} + 1) d x

integral of (ln(x^4))/(x^7)

\int \frac{ln ( x ^{4} )}{x ^{7}} d x

integral of-e^xsin(e^x)

\int - e^{x} sin (e^{x}) d x

Frequently Asked Questions (FAQ)

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