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In this specific example one would need to use the u substitution method.
* Set u to be x - 3 * Derive x - 3 * u = x - 3 * du = dx Now that we have integrated u we can remove the x - 3 and substitute in u and remove the dx and substitute in du.
This is what we have after substituting:
* (the integrand of) tan(u)du Now integrate tan(u)du
* the Integral of tan(u)du is: * sec2(u) Now resubstitute what we set as u. In this case we set x - 3 to u. This will give us our final answer and integral of tan(x-3)dx.
* sec2(x - 3)
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