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int(sin^(3)x)/((cos^(4)x+3cos^(2)x+1)tan^(-1)(secx+cosx))dx= |
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Answer» `tan^(-1)(SECX+cosx)+C` `I=int_(sin^(3)x)/((COS^(4)x+3cos^(2)x+1)tan^(-1)(secx+cosx))dx` `impliesI=int((sin^(3)x)/(cos^(2)x))/((cos^(2)x+3+sec^(2)x)tan^(-1)(secx+cosx))dx` `impliesI=int1/(1+(secx+cosx)^(2))XX(sinx(1-cos^(2)x))/(cos^(2)x)xx1/(tan^(-1)(secx+cosx))dx` `impliesI=int1/(tan^(-1)(secx+cosx))xx1/(1+(secx+cosx))^(2)xx(tanx secx -sinx)dx` `impliesI=int1/(tan^(-1)(secx+cosx))d{tan^(-1)(secx+cosx)}` `impliesI=log|tan^(-1)(secx+cosx)|+C` |
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