How do you integrate int x*2^x by integration by parts method? Calculus Techniques of Integration Integration by Parts 1 Answer Eddie Aug 3, 2016 =2^x/ (ln 2) ( x - 1/ (ln 2) ) + C Explanation: firstly know that d/dx ( a ^x ) = ln a \ a^x So int x*2^x \ dx = int x d/dx( 1/ ln 2 2^x) \ dx = x/ ln 2 2^x - int d/dx(x) 1/ ln 2 2^x\ dx = x/ ln 2 2^x - 1/ ln 2 int 2^x\ dx = x/ ln 2 2^x - 1/ ln 2 int d/dx( 1/ ln 2 2^x)\ dx = x/ ln 2 2^x - 2^x 1/( ln 2 )^2+ C =2^x/ (ln 2) ( x - 1/ (ln 2) ) + C 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 1239 views around the world You can reuse this answer Creative Commons License