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

The integral of (1-x)(2+x^3) is 2x+(x^4)/4-x^2-(x^5)/5+C

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

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

2 x + \frac{x ^{4}}{4} - x^{2} - \frac{x ^{5}}{5} + C

Solution steps

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

Expand

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

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

\int 2 d x = 2 x

\int x^{3} d x = \frac{x ^{4}}{4}

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

\int x^{4} d x = \frac{x ^{5}}{5}

= 2 x + \frac{x ^{4}}{4} - x^{2} - \frac{x ^{5}}{5}

Add a constant to the solution

= 2 x + \frac{x ^{4}}{4} - x^{2} - \frac{x ^{5}}{5} + C

\frac{x ^{2} + 6}{5 x - 2}

\int e^{(y^{2})} d y

\int_{0}^{1} (x - x) d x

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

e^{(\frac{1}{t} l n (\frac{5 ^{t} + 1 3 ^{t}}{2}))}

What is the integral of (1-x)(2+x^3) ?
The integral of (1-x)(2+x^3) is 2x+(x^4)/4-x^2-(x^5)/5+C