Simplifying a trigonometric product

[Manni]

Was just double checking if we can simplify this in the following way,

∫ sinx * √(1 + cos²x) dx = ∫ sinx * (1 + cosx) dx

 

[SammyS]

Was just double checking if we can simplify this in the following way,

∫ sinx * √(1 + cos²x) dx = ∫ sinx * (1 + cosx) dx

No.

Is $\sqrt{3^2+4^2}=7\ ?$ No !

$\sqrt{3^2+4^2}=\sqrt{25}=5\ .$.

To solve that integral, use substitution .

Ask your self, what's the derivative of cos(x) ?