Question

integrate (x - x³)

Answer 1

integrate x and integrate -x^3 separately

Answer 2

\[\int\limits (x-x^3)dx=\frac{1}{2}x^2-\frac{1}{4}x^4+C\]

Answer 3

Anti-differentiate.

Answer 4

Work backwards from differentiating. How would you get x from the first place? You would differentiate x^2. but there's no 2 at the front so you put a half at the front to cancel at the 2.

Answer 5

Same goes for x^3. You would originally have x^4 but there's no 4 at the front so you bring a quarter down the front to cancel it out.

Answer 6

cancel out*

Answer 7

\[\int\limits_{}^{}x ^{n}dx=x ^{n+1}/(n+1)\]

Answer 8

\[\int\limits_{}^{}(x-y)dx=\int\limits_{}^{}(x)dx-\int\limits_{}^{}(y)dx\]