# X dx csc x c and some require reciprocal identities

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x dx= -csc x + CAnd some require reciprocal identities and integrate to natural logs.sec xdx = ln |sec x + tan x| + Ccsc xdx = -ln |csc x + cot x| + Ccotx dx= ln|sin x| + Ctanx dx= -ln|cos x| + CAll should be memorized; remember that you can always check an integrand by differentiating.Sine and CosineIntegral: sin(2x)dxIntegral: cos(4x)Solution: 12cos(2x)+CSolution:14sin(4x)+Integral:xsin(x2+5)dxIntegral: 9x2cos(x315)dx
dx
C
12) Use u-substitution and the above examples to finde2xsin(e2x)dx13) Use u-substitution to find3xcos(x2+8)dx
Secant and Cosecant, Tangent and CotangentExamine each example below and answer the following questions.IntegralSolution
ii.x4