How do you find the integral of $\frac{cos (x)}{\sqrt{1 + {sin}^{2} (x)}}$ $cos(x) / sqrt(1+sin^2(x)$ ?

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Answer 1 · 2018-05-07T17:32:41

$ln ∣ sin x + \sqrt{1 + {sin}^{2} x ∣ ∣} + C$ $ln|sinx+sqrt(1+sin^2x|)+C$ .

If we subst. $sinx=t. :. cosxdx=dt$ .

$:. intcosx/sqrt(1+sin^2x)dx$ ,

$=int1/sqrt(1+t^2)dt$ ,

$=ln|t+sqrt(1+t^2)|$ .

But, $t=sinx$ .

$:. I=ln|sinx+sqrt(1+sin^2x|)+C$ .

Answer 2 · 2018-05-07T17:41:01

$I=ln|sinx+sqrt(1+sin^2x)|+c$

Here,

$I=intcosx/sqrt(1+sin^2x)dx$

Let, $sinx=u=>cosxdx=du$

$I=int1/sqrt(1+u^2)du$

$=ln|u+sqrt(1+u^2)|+c$

Subst,back, $u=sinx$

$I=ln|sinx+sqrt(1+sin^2x)|+c$

How do you find the integral of cos(x) / sqrt(1+sin^2(x)cos(x)√1+sin2(x)cos(x) / sqrt(1+sin^2(x)?