Question

Integral de cos^2(x) + sen(x).dx

Answer 1

Resposta:

∫ cos²(x)+sen(x) dx

=∫ cos²(x) dx + ∫ sen(x) dx

****cos(2x)=2cos²(x)-1  ==> cos²(x)=[cos(2x)+1]/2

=∫ [cos(2x)+1]/2 dx + ∫ sen(x) dx

=(1/2)*∫ [cos(2x) dx + (1/2) ∫ dx + ∫ sen(x) dx

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∫ [cos(2x) dx

u=2x ==> du=2dx

∫ [cos(u) du/2 ==> (1/2)*sen(u)  ..Como u=2x ==> (1/2)* sen(2x)

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=(1/2)*[(1/2)* sen(2x)] + (1/2) x - cos(x) + constante

=(1/4)* sen(2x) + x/2 - cos(x) + constante

Answer 2

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