1. ## integrals

Determine the integrals:

curently studying this module and looking at a few examples.
if someone could explain when working these out, would help be gratefully in doing other examples: three examples thank you

∫×3 + 3 dx
3 ×3

∫cos(4x+7) dx

∫ 3xsinx dx

2. The first one is unreadable...

For the second, make the substitution $\displaystyle u = 4x + 7 \implies du = 4\,dx$

For the third, you need to use integration by parts...

3. first example has come out wrong it is meant to me Sum of x3 over 3 + 3dx over xcubed

4. Do you mean $\displaystyle \int{\frac{x^3}{3} + \frac{3}{x^3}\,dx}$? If so, rewrite it as $\displaystyle \int{\frac{1}{3}x^3 + 3x^{-3}\,dx}$ and go from there...

5. yep that is correct