Integration by Parts, step by step
Choose u to become simpler when differentiated.
- Split the integrandWrite it as u dv. One factor to differentiate, one to integrate.
- Choose u by LIATELog, Inverse trig, Algebraic, Trig, Exponential — earlier wins.
- Find du and vDifferentiate u, integrate dv. Leave the constant of integration out here.
- Apply the formulaIntegral of u dv = uv − integral of v du. The new one should be easier.
- Repeat, or solve for ISome integrals return to themselves — rearrange for I rather than looping.
Worked: with u = x, the integral of x e^x dx is x e^x − the integral of e^x dx, giving e^x(x − 1) + C.
Questions about the Integration by Parts poster
- What’s on the Integration by Parts poster?
- 5 numbered steps. Choose u to become simpler when differentiated. Split the integrand — Write it as u dv. One factor to differentiate, one to integrate.; Choose u by LIATE — Log, Inverse trig, Algebraic, Trig, Exponential — earlier wins.; Find du and v — Differentiate u, integrate dv. Leave the constant of integration out…; Apply the formula — Integral of u dv = uv − integral of v du. The new one should be e…; Repeat, or solve for I — Some integrals return to themselves — rearrange for I rather…. Worked: with u = x, the integral of x e^x dx is x e^x − the integral of e^x dx, giving e^x(x − 1) + C.
- Who is the Integration by Parts poster for?
- Integration by Parts belongs to the Mathematics section rather than to a school year, because math is not something one grade owns. Anyone learning calculus can pin it up — a beginner, a student mid-course, or someone revising years later.
- When should you use the Integration by Parts poster?
- When the integrand is a product of two unrelated kinds of function. A wall chart earns its place by being glanceable from where the work is happening, so Integration by Parts belongs on the wall where that math work actually happens, within glancing distance, rather than filed away.
- What other posters go with Integration by Parts?
- The Chain Rule, Derivative Rules and Fundamental Theorem sit alongside Integration by Parts in the Mathematics section. Printed together they make a wall rather than a single sheet, which is how a reference set actually gets used.The Chain RuleDerivative RulesFundamental Theorem
- Is the Integration by Parts poster free to download and print?
- Yes. Integration by Parts downloads as a free PDF with no account, no email and no watermark, like everything else in the Mathematics section. Print as many copies as you like for a home, a classroom, a library or a tutoring group; reselling the file is the only thing the licence rules out.Read the licence
- What size does the Integration by Parts poster print at?
- Integration by Parts is a vector PDF laid out for US Letter, and prints on A4 with Fit to page — the same file, no separate download. Because every mark on it is drawn rather than photographed, it stays sharp enlarged to A3, A2 or A1 at a copy shop. Colour carries emphasis only, so a greyscale print of Integration by Parts loses nothing.Printing guide
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