Techniques of Integration: Integration by Parts, Products of Powers of Trigonometric Functions Use integration by parts to integrate functions. Integrate products of powers of trigonometric functions. Evaluate ∫csc3xcot5xdx

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Techniques of Integration: Integration by Parts, Products of Powers of Trigonometric Functions  Use integration by parts to integrate functions.  Integrate products of powers of trigonometric functions.  Evaluate  ∫csc3xcot5xdx

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Step1  Given the integral  ∫csc3xcot5xdx  To Evaluate the integral  I=∫csc3xcot5xdx  =∫−csc⁡xcot⁡x{(−csc2x{(cot2x})})dx  =∫−csc⁡xcot⁡x{(−csc2x{(csc2x−1})2})dx  Step 2  Substitute  u=csc⁡x  du=−csc⁡xcot⁡xdx  I=−∫u2{(u2−1})2du  I=−∫{(u6−2u4+u2})du  =−{[u77−2{(u55})+u33}]+c  =−csc7x7+2csc5x5−csc3x3+c

Techniques of Integration: Integration by Parts, Products of Powers of Trigonometric Functions Use integration by...

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