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Popular Calculus >

integral of-x^2+3x+4

Solution

\int - x^{2} + 3 x + 4 d x

Solution

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

Solution steps

\int - x^{2} + 3 x + 4 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 3 x d x + \int 4 d x

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

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

\int 4 d x = 4 x

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

Add a constant to the solution

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

Graph

Popular Examples

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

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

integral of-4/t

\int - \frac{4}{t} d t

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

\int \frac{2 x}{( 2 x ^{2} - 5 ) ^{2}} d x

integral of 1/(sqrt((w^2+5)^3))

\int \frac{1}{( w ^{2} + 5 ) ^{3}} d w

integral of 1/(ysqrt(y^2-16))

\int \frac{1}{y y ^{2} - 16} d y

Frequently Asked Questions (FAQ)

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