Question

what is the integration of 1/sinx.cosx dx​

Answer 1

Answer:

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Answer 2

Given:

1 / (sinx.cosx).dx.

To Find:

The integration of the given question.

Solution:

Let's divide the numerator and the denominator by cos^2x.

I = (1/cos^2x) / (sinx.cosx/ cos^2).dx.

I = sec^2x / tanx. dx.

Now,

Let tanx = t,

and, sec^2x .dx = dt.

dx = dt/sec^2x.

So,

I = dt/ t.

By integrating the above equation,

I = log t + c.

Since, t = tanx.

So,

I = log | tanx | + c.

Hence, the integration of 1/ (sinx.cosx) dx is log | tanx | + c.