What is the antiderivative of lnxx12? Calculus Techniques of Integration Integration by Parts 1 Answer Andrea S. Jun 27, 2018 ∫lnxx12dx=2√x(lnx−2)+C Explanation: Integrate by parts: ∫lnxx12dx=∫lnx⋅x−12dx ∫lnxx12dx=2∫lnx⋅ddx(x12)dx ∫lnxx12dx=2x12lnx−2∫x12⋅ddx(lnx)dx ∫lnxx12dx=2x12lnx−2∫x12⋅1xdx ∫lnxx12dx=2x12lnx−2∫x−12dx ∫lnxx12dx=2x12lnx−4x+12+C ∫lnxx12dx=2x12(lnx−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 1605 views around the world You can reuse this answer Creative Commons License