sec(x)dx
To find the integral of sec(x)dx, you can use the technique of substitution
To find the integral of sec(x)dx, you can use the technique of substitution. Let’s take a step-by-step approach:
Step 1: Identify a suitable substitution:
We know that the derivative of sec(x) is sec(x)tan(x). So let’s choose u = sec(x) and du = sec(x)tan(x)dx.
Step 2: Rewrite the integral using the substitution:
Using the substitution u = sec(x), we can rewrite the integral as ∫du.
Step 3: Solve the integral:
Now, we can solve the integral of du, which is simply u + C, where C is the constant of integration.
Step 4: Final substitution:
Using the substitution u = sec(x), we can replace u to get the final answer:
∫ du = sec(x) + C.
Therefore, the integral of sec(x)dx is sec(x) + C, where C is the constant of integration.
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