Solving for ∫(sec(x)tan(x))dx using the u-substitution method

∫(secxtanx)dx

To integrate ∫(sec(x)tan(x))dx, we can apply the u-substitution method

To integrate ∫(sec(x)tan(x))dx, we can apply the u-substitution method.

Step 1: Determine u and du
Let u = sec(x)
Then, du = sec(x)tan(x)dx

Step 2: Rewrite the integral
We can rewrite the integral in terms of u as follows:
∫(sec(x)tan(x))dx = ∫du

Step 3: Integrate
Now, since the integral has been simplified to ∫du, we can directly integrate to get the final result:
∫du = u + C

Step 4: Substitute back
To obtain the final answer in terms of x, we need to substitute back u = sec(x):
∫(sec(x)tan(x))dx = sec(x) + C

Therefore, the final answer is sec(x) + C, where C is the constant of integration.

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