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Integrate cos2x/sinx dx

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Integrate cos2x/sinx dx

Integration of cos2x/sinx dx

To integrate cos2x/sinx dx, we need to use the substitution method. Let's start by writing the integral in a different form:

cos2x/sinx = (cosx)^2/sinx = cosx/sinx * cosx = cotx * cosx

Step 1: Substitute u = sinx

Let u = sinx, then du/dx = cosx. We can rewrite the integral in terms of u:

∫ cos2x/sinx dx = ∫ cotx * cosx dx = ∫ cotx * du

Step 2: Integrate the new function

We can now integrate the new function:

∫ cotx * du = ln|sinx| + C

Step 3: Substitute back to x

Finally, we substitute back to x:

∫ cos2x/sinx dx = ln|sinx| + C

Conclusion

Integrating cos2x/sinx dx involves using the substitution method. We first substitute u = sinx, then integrate the new function, and finally substitute back to x. The final answer is ln|sinx| + C.

Community Answer

Integrate cos2x/sinx dx

Log(cosecx - cotx)+ 2cosx + c

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