More than one answer to integration

Question

$$\int \sec^4(x)\tan(x)\,dx$$

For this question I use substitution method to solve but my answer was different (may be because of different approach).My answer was $(\sec^4x)/4 + C$. Can someone tell me if there are any other answers to this problem and how they are equivalent?

Answer 1

hint: Write your integrand as $$\tan(x)(\tan(x)^2+1)\sec(x)^2$$ and substitute $$u=\tan(x)$$ then we get $$\int u(u^2+1)du$$ and this is easy to solve.

Answer 2

Write the integral as $$ \int (1+\tan^2x)\tan x\sec^2x\, dx $$ and make the substitution $u=\tan x$ to get that the integral equals $$ \int u(1+u^2)\, du=\int u+u^3\, du $$ which you should be able to integrate.