What is the integral of (1-2x)(3+x) ?

The integral of (1-2x)(3+x) is 3x-(5x^2)/2-(2x^3)/3+C

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

\int (1 - 2 x) (3 + x) d x

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

Solution steps

\int (1 - 2 x) (3 + x) d x

Expand

(1 - 2 x) (3 + x) : 3 - 5 x - 2 x^{2}

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

\int 3 d x = 3 x

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

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

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

Add a constant to the solution

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

sec^{2} (t)

\int \frac{cos ( ln ( x + 1 ) )}{x + 1} d x

\int \frac{3}{3 x} d x

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

\int \frac{x + 7}{x - 1} d x

What is the integral of (1-2x)(3+x) ?
The integral of (1-2x)(3+x) is 3x-(5x^2)/2-(2x^3)/3+C