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# Solving an Integral arcsec(sqrt(x2+4x+5))dx?

The picture attached shows the integral Please show work! I want to understand each step:) Thank you!

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- VamanLv 71 month agoFavourite answer
sec(sqrt(x2+4x+5))dx? define y=sec(sqrt(x2+4x+5))Let us simplify x^2+4x+5=x^2+4x+4+1=(x+2)^2+1. Let x+2= tan y. (x+2)^2+1= sec^y. sec^(-1) Sqrt (x^2+4x+5)=sec^(-1) sec y= y, dy= sec^2(x+2)

The integral = tan (x+2) sec^2(x+2)dx

sin(x+2)/cos^3(x+2) dx= -1/(2 cos^(x+2)) + constant. Please check the method.

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