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Popular >

integral of (x+3)(x-7)

Solution

\int (x + 3) (x - 7) d x

Solution

\frac{x ^{3}}{3} - 2 x^{2} - 21 x + C

Solution steps

\int (x + 3) (x - 7) d x

Expand

(x + 3) (x - 7) : x^{2} - 4 x - 21

= \int x^{2} - 4 x - 21 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 4 x d x - \int 21 d x

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

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

\int 21 d x = 21 x

= \frac{x ^{3}}{3} - 2 x^{2} - 21 x

Add a constant to the solution

= \frac{x ^{3}}{3} - 2 x^{2} - 21 x + C

Popular Examples

area x^2-3,5-x^2 area

x^{2} - 3, 5 - x^{2}

(\partial)/(\partial x)(x^2+2y^2+xy^2+1)

\frac{\partial}{\partial x} (x^{2} + 2 y^{2} + x y^{2} + 1)

f (t) = 3 sin (2 t)

integral of x^2-5x+6

\int x^{2} - 5 x + 6 d x

(\partial)/(\partial x)(x^{1/4}y^{3/4})

\frac{\partial}{\partial x} (x^{\frac{1}{4}} y^{\frac{3}{4}})

Frequently Asked Questions (FAQ)

What is the integral of (x+3)(x-7) ?
The integral of (x+3)(x-7) is (x^3)/3-2x^2-21x+C