How do you integrate #(e^sin(x))cos(x) dx#? Calculus Techniques of Integration Integration by Parts 1 Answer Shwetank Mauria May 11, 2016 #inte^(sinx)cosxdx=e^sinx# Explanation: Let #u=sinx#, then #du=cosxdx# and #inte^(sinx)cosxdx=inte^udu=e^u=e^sinx# Answer link Related questions How do I find the integral #int(x*ln(x))dx# ? How do I find the integral #int(cos(x)/e^x)dx# ? How do I find the integral #int(x*cos(5x))dx# ? How do I find the integral #int(x*e^-x)dx# ? How do I find the integral #int(x^2*sin(pix))dx# ? How do I find the integral #intln(2x+1)dx# ? How do I find the integral #intsin^-1(x)dx# ? How do I find the integral #intarctan(4x)dx# ? How do I find the integral #intx^5*ln(x)dx# ? How do I find the integral #intx*2^xdx# ? See all questions in Integration by Parts Impact of this question 43917 views around the world You can reuse this answer Creative Commons License