Mathematics: To evaluate ∫ 3x2 cos (2x3 - 4) dx, it is necessary to let

To evaluate ∫ 3x2 cos (2x3 - 4) dx, it is necessary

Ответ:

awesomegrill

13.03.2022

If we were to take y=2x^3-4

, then we have $\mathrm dy=6x^2\,\mathrm dx$ . So in the integral, we could write

$\displaystyle\int3x^2\cos(2x^3-4)\,\mathrm dx=\int2(3x^2)\cos(2x^3-4)\,\mathrm dx=2\int\cos y\,\mathrm dy=2\sin y+C$

Then back-substituting to get the antiderivative in terms of