What is the antiderivative of ln(2x)x12? Calculus Techniques of Integration Integration by Parts 1 Answer Eddie Feb 9, 2017 =2x12(ln(2x)−2)+C Explanation: ∫ln(2x)x12dx We set it up for IBP: =∫ln(2x)ddx(2x12)dx Applying the IBP: =2x12ln(2x)−∫ddx(ln(2x))(2x12)dx =2x12ln(2x)−∫1x⋅2x12dx =2x12ln(2x)−2∫x−12dx =2x12ln(2x)−2⋅2x12+C =2x12(ln(2x)−2)+C Answer link Related questions How do I find the integral ∫(x⋅ln(x))dx ? How do I find the integral ∫(cos(x)ex)dx ? How do I find the integral ∫(x⋅cos(5x))dx ? How do I find the integral ∫(x⋅e−x)dx ? How do I find the integral ∫(x2⋅sin(πx))dx ? How do I find the integral ∫ln(2x+1)dx ? How do I find the integral ∫sin−1(x)dx ? How do I find the integral ∫arctan(4x)dx ? How do I find the integral ∫x5⋅ln(x)dx ? How do I find the integral ∫x⋅2xdx ? See all questions in Integration by Parts Impact of this question 1468 views around the world You can reuse this answer Creative Commons License