What is the integral of 10000-2(2q+q^3) ?

The integral of 10000-2(2q+q^3) is 10000q-2(q^2+(q^4)/4)+C

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integral of 10000-2(2q+q^3)

\int 10000 - 2 (2 q + q^{3}) d q

10000 q - 2 (q^{2} + \frac{q ^{4}}{4}) + C

Solution steps

\int 10000 - 2 (2 q + q^{3}) d q

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 10000 d q - \int 2 (2 q + q^{3}) d q

\int 10000 d q = 10000 q

\int 2 (2 q + q^{3}) d q = 2 (q^{2} + \frac{q ^{4}}{4})

= 10000 q - 2 (q^{2} + \frac{q ^{4}}{4})

Add a constant to the solution

= 10000 q - 2 (q^{2} + \frac{q ^{4}}{4}) + C

What is the integral of 10000-2(2q+q^3) ?
The integral of 10000-2(2q+q^3) is 10000q-2(q^2+(q^4)/4)+C