Question

PLS ANSWER THIS ANYONE?





how do I integrate cos(x+a)/sinx dx

Answer 1

Answer:

Cosa logSinx - x Sina + c

Step-by-step explanation:

To find---> ∫ Cos( x + a ) / Sinx dx

Solution---->

Formula applied--->

1) Cos( x + a ) = Cosx Cosa - Sinx Sina

2) Cotx = Cosx / Sinx

3) ∫ Cotx dx = logSinx + C

4) ∫ 1 dx = x + c

Now returning to original problem,

∫ Cos(x + a ) / Sinx dx

= ∫ (Cosx Cosa - Sinx Sina ) / Sinx dx

= ∫( Cosx Cosa / Sinx ) dx - ∫ ( Sinx Sina / Sinx ) dx

= Cosa ∫( Cosx / Sinx ) dx - Sina ∫ (Sinx / Sinx )dx

= Cosa ∫ Cotx dx - Sina ∫ 1 dx

= Cosa logSinx - Sina ( x ) + c

= Cosa logSinx - x Sina + c

Additional information--->

1) ∫ xⁿ dx = xⁿ⁺¹ / ( n + 1 ) + c

2) ∫ eˣ dx = eˣ + c

3) ∫ aˣ dx = aˣ / loga + c

4) ∫ Sinx dx = - Cosx + c

5) ∫ Cosx dx = Sinx + c

6) ∫ sec²x dx = tanx + c

7) ∫ Secx tanx dx = Secx + c

8) ∫cosec²x dx = - Cotx + c

9) ∫Cosecx cotx dx = - Cosecx + c