MATH 1007 Lecture Notes - Lecture 15: Antiderivative
6 Apr 2016
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Integral of udv = uv integral of vdu. Let u = x du = dx. Du=exdx v=ex we didn"t write the 1 here. **choose the right u and the right dv choose the easier one as u. Choose u = lnx du = 1/x. = lnx: x4/4 integral x4(1/x)dx. = x4/4: lnx integral x3dx. = x4/4 lnx : x4/4 + c. Let u = (lnx)2 du = 2lnx (1/x)dx. = x(lnx)2 2(xlnx x) + c from previous example, we know = x( e2x) integral of e2xdx. = x/2: e2x integral of e2xdx. Since lnx is really hard to ind the aniderivaive of = lnx(x2/2) integral of x2: (1/x) dx. = x2/2: lnx x2/2 + c. = x2/2: lnx x2/4 + c. = sinx ln(sinx) integral of sinx: (1/sinx)cosxdx. Let u = x2 du = 2xdx. = x2ex 2x2ex 2ex + c1. = exx3 3[exx2 2[xex - ex]] + c. = exx3 3exx2 + 6xex - 6ex + c.
