Question

1.∫ x³(x+1)dx
2.∫ (1-cot²x)dx
3.∫ cosx(tan x + sec x) dx
4.∫ dx/√5x+8 using u= 5x+8 and using u= √5x+5

Answer 1

1. is integral x^4 dx + integral x dx

2. same deal, split into sum of two integrals
integral of cot^2 x = (-1/x)cot x - x

3. yet again
cos*sin/cos = cos :)
cos * 1/cos = 1 :)

4. I think you have a typo and I do not know what is u and what is du or actually what is in the original denominator

do you mean
dx / [(5x)^.5 + 8 ]
or what