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We Then Use The Substitution U= Cosx=)du= Sinxdxto Get Z Sin5 Xcos2 Xdx= Z U2 2u4 + U6 Du = U3 3 2u5 5 + U7 7 + C = Cos3 X 3 + 2cos5 X 5 Cos7 X 7 + C Example 310 Find R Sin2 Xdx This Is The Case When The Powers Of Sine And Cosine Are Even (the Power Of Cosine Being 0). We Use 1th, 2024
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It Might Be Helpful To Make A Substitution. 1. R E2 1 P Xln(x)dx 4 9 (1+2e 3) 2. R 1 0 X P 1+xdx 4 15 (1+ P 2) Discuss: Does The Best Strategy For Solving Each Of The Following Integrals Use Substitution, Integration By Parts, Both, Or Neither? 1. R Xln(x)dx: IBP (u = Lnx) 2. R Ln(x) X Dx: Sub U = Lnx 3. R 1 Xln(x 1th, 2024
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(c)(even Power Of Secant) Evaluate Tan5 Xsec4 Xdx Using The Substitution U = Tanx. Solution: We Have Du = Sec2 Dx So Tan5 Xsec4 Xdx = Tan5 Xsec2 X Sec2 Xdx = U5 1+u2 Du = U5 +u7 Du = 1 6 U6 + 1 8 U8 +C = 1 6 Tan6 X+ 1 8 Tan8 X+C : (d)(odd Power Of Tangent) Write Tan5 Xsec3 Xdx In The Form 1th, 2024
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All Values Of X, This Last Expression Is An Identity, And Identities Are One Of The Topics We Will Study In This Chapter. Cos2 X 1 4 Sin X 1 2 Sin X Y Cos2 X And Y 1 Sin4 X 1 Sin2 X 795 Trigonometric ... Proving Trigonometric Identities Worksheet With Answers 1th, 2024
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