Antiderivative

[dear2009]

Hello Math Participants,



I am having trouble with this antiderivative problem
antiderivative sign [(3)(sec^2)(3x) + 1/6(x^5/6)] dx = ?



This is what I have tried to do

3(x^3 sec^2 x) dx = tan x + C


3x^3tanx + C

I am not sure what to do afterwards, so any help would be greatlyappreciated

 

[Deleted member 4993]

Hello Math Participants,



I am having trouble with this antiderivative problem
antiderivative sign [(3)(sec^2)(3x) + 1/6(x^5/6)] dx = ?



This is what I have tried to do

3(x^3 sec^2 x) dx = tan x + C <<<< This is not correct


3x^3tanx + C

I am not sure what to do afterwards, so any help would be greatlyappreciated

$\displaystyle \int [3sec^2(3x) + \frac{x^{\frac{5}{6}}}{6}] dx$

$\displaystyle = \int 3sec^2(3x)dx + \int\frac{x^{\frac{5}{6}}}{6} dx$

$\displaystyle = \int sec^2(u)du + \frac{x^{(1+\frac{5}{6})}}{6(1+\frac{5}{6})}$

$\displaystyle = tan(u) + \frac{x^{(1+\frac{5}{6})}}{6(1+\frac{5}{6})}$ ...... now continue.....