Question

Calcule a integral

l) $\int\ {} \frac{2~cot~gx~-~3sen^2x}{senx} \, dx$

Answer 1

Oi Lucas

∫ (2cotg(x) - 3sen²(x))/sen(x) dx = 

2 ∫ cotg(x)csc(x) dx - 3 ∫ sen(x) dx = 

2 ∫ cos(x)/sen²(x) dx - 3 ∫ sen(x) dx = 

 ∫ cos(x)/sen²(x) dx 

 u = sen(x) , du = cos(x)dx

 ∫ du/u² = -1/u 

 ∫ cos(x)/sen²(x) dx = -1/sen(x) 

 ∫ sen(x) dx = -cos(x) 

 2 ∫ cos(x)/sen²(x) dx - 3 ∫ sen(x) dx = -2/sen(x) + 3cos(x) + C

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