How do I evaluate the indefinite integral intcot^5(x)*sin^4(x)dx ? Calculus Introduction to Integration Integrals of Trigonometric Functions 1 Answer Monzur R. Apr 23, 2018 cos^2x+1/4sin^4x+lnabssinx+"c" Explanation: cot^5xsin^4x=cos^5x/sin^5xsin^4x=cos^5x/sinx=cos^4xcotx=(1-sin^2x)^2cotx=(1-2sin^2x+sin^4x)cot=cotx-2sinxcosx+sin^3xcosx So intcot^5xsin^4xdx=intcotxdx-int2sinxcosxdx+intsin^3xcosxdx Now let u=sinx and du=cosxdx and v=cosx and dv=-sinxdx intcotxdx+int-2sinxcosxdx+intsin^3xcosxdx=lnabssinx int2vdv +intu^3du=lnabssinx+v^2+1/4u^4+"c"=cos^2x+1/4sin^4x+lnabssinx+"c" Answer link Related questions How do I evaluate the indefinite integral intsin^3(x)*cos^2(x)dx ? How do I evaluate the indefinite integral intsin^6(x)*cos^3(x)dx ? How do I evaluate the indefinite integral intcos^5(x)dx ? How do I evaluate the indefinite integral intsin^2(2t)dt ? How do I evaluate the indefinite integral int(1+cos(x))^2dx ? How do I evaluate the indefinite integral intsec^2(x)*tan(x)dx ? How do I evaluate the indefinite integral inttan^2(x)dx ? How do I evaluate the indefinite integral int(tan^2(x)+tan^4(x))^2dx ? How do I evaluate the indefinite integral intx*sin(x)*tan(x)dx ? How do I evaluate the indefinite integral intsin(x)/(cos^3(x))dx ? See all questions in Integrals of Trigonometric Functions Impact of this question 12977 views around the world You can reuse this answer Creative Commons License