Integrate: sin^-1 ( 2x+2 / square root 4x^2+8x+13)

Answers (1)

Solution:    

             I=int sin^-1(frac2x+2sqrt4x^2+8x+13)dx

    \ \ I=int sin^-1(frac2x+2sqrt(2x+2)^2+3^2)dx\ \ Put hspace0.2cm2x+2=3	an 	hetaRightarrow 2dx=3sec^2	heta d	heta\ \ I=intsin^-1(frac3	an 	heta3 sec	heta)frac32sec^2	heta d	heta\ \ I=frac32int 	heta cdot sec^2	heta d	heta=frac32[	heta 	an 	heta-ln left | sec 	heta 
ight |]\ \ I=frac32[frac2x+23	an^-1(frac2x+23)-ln sqrt1+(frac2x+23)^2]+c

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