Math question integration

how to intergrate 1/(3+4x)^4. isit using u subtitution, u=3+4x or (3 + 4x)^4

u=3+4x
du=4dx
so
∫ 1/(3 + 4x)^4dx=1/4∫ (1/u^4)du
1/4*∫u^-4du
1/4 *(u^-3)/-3 since ∫x^n=(x^n+1)/n+1 provided x not = 1
or
-1/12 *(3+4x)^-3

and you are not right in lnu^4 thing

There is absolutely no need to use substitution here, simply integrate as normal then divide by the derivative of the bracket.

Integrate this expression using the power rule:
∫ 1 / (3 + 4x)⁴ = -1 / [12(3 + 4x)³] + C
∫ 1 / (3 + 4x)⁴ = C - 1 / [12(4x + 3)³]

Use u=3+4x. Then dx = du/4.