Question

50 points question solve fastly on copy....

Answer 1

I hope it is correct

Answer 2

Answer:

Step-by-step explanation:

How can I solve this integral (dx/1+sinx)?

∫dx1+sinx=∫dxsin2x2+2sinx2cosx2+cos2x2=∫dx(sinx2+cosx2)2=∫dx(2–√sin(x2+π4))2=12∫csc2(x2+π4)dx=−cot(x2+π4)+C=−1−tanx21+tanx2+C=sinx2−cosx2sinx2+cosx2+C=sinx−1cosx+C

In fact, all expressions with +C can be the answer, but there are many forms of trigonometric answers.

Here's another faster way:

∫dx1+sinx=∫(1−sinx)dxcos2x=∫sec2xdx−∫secxtanxdx=tanx−secx+C

which is consistent with the above approach