Question

Simply, 20² +50-1+8X+X²+7_6x4
3-322)​

Answer 1

Answer:

Setting u=−x2−8x−7, you have du=(−2x−8)dx, so (x+4)dx=−du2. So write

∫xdx−x2−8x−7−−−−−−−−−−−√=∫(x+4)dx−x2−8x−7−−−−−−−−−−−√+∫−4dx−x2−8x−7−−−−−−−−−−−√.

Use the substitution above to do the first integral on the right side.

For the second integral, you have

∫−4dx9−(x+4)2−−−−−−−−−−√=−4∫dx/31−(x+43)2−−−−−−−−−√.

So let sinθ=x+43, and then cosθdθ=dx3. The radical becomes 1−sin2θ−−−−−−−−√=cosθ.