∫(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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