How do I evaluate int cos^5(x) sin^4(x) dx? Calculus Techniques of Integration Integration by Trigonometric Substitution 1 Answer maganbhai P. Apr 20, 2018 I=sin^5x/5-(2sin^7x)/7+sin^9x/9+c Explanation: Here, I=intcos^5xsin^4xdx =intsin^4x(cos^2x)^2cosxdx =intsin^4x(1-sin^2x)^2cosxdx Let, sinx=t=>cosxdx=dt So, I=intt^4(1-t^2)^2dt =int(t^4(1-2t^2+t^4)dt =int(t^4-2t^6+t^8)dt =t^5/5-2(t^7/7)+t^9/9+c..towhere,t=sinx =sin^5x/5-(2sin^7x)/7+sin^9x/9+c Answer link Related questions How do you find the integral int1/(x^2*sqrt(x^2-9))dx ? How do you find the integral intx^3/(sqrt(x^2+9))dx ? How do you find the integral intx^3*sqrt(9-x^2)dx ? How do you find the integral intx^3/(sqrt(16-x^2))dx ? How do you find the integral intsqrt(x^2-1)/xdx ? How do you find the integral intsqrt(x^2-9)/x^3dx ? How do you find the integral intx/(sqrt(x^2+x+1))dx ? How do you find the integral intdt/(sqrt(t^2-6t+13)) ? How do you find the integral intx*sqrt(1-x^4)dx ? How do you prove the integral formula intdx/(sqrt(x^2+a^2)) = ln(x+sqrt(x^2+a^2))+ C ? See all questions in Integration by Trigonometric Substitution Impact of this question 15657 views around the world You can reuse this answer Creative Commons License