Handwritten-style notes that break calculus, linear algebra, and differential equations into the annotated steps your professor never had time for — built for the 2 AM study session.
What most students try first
∫ x · eˣ dx
= x · eˣ + C
✗ Forgot to integrate — treated it like a product
= eˣ · (x + 1)
✗ Sign error — missed the minus in uv − ∫v du
These aren't careless mistakes — they're gaps in how the method was explained.
What the method actually requires
u = x → du = dx
dv = eˣ dx → v = eˣ
= x·eˣ − ∫eˣ dx
Every Proof guide shows you exactly where the step breaks — and why.
The algebraic derivation
Integration by parts comes from the product rule:
The formula isn't magic — it's just the product rule flipped around. Once you see that, you never forget it.
Why it works — geometrically
The blue area + red area = the whole rectangle. That's the formula, drawn.
Every abstract rule has a picture behind it. Proof shows you both.
Try it yourself — timed
Evaluate: ∫ x · cos(x) dx
What you're building toward
Limits, derivatives, integration techniques, series, multivariable. 240+ worked examples.
Eigenvectors, matrix decompositions, vector spaces. Visual proofs alongside every theorem.
ODEs, systems, Laplace transforms. The exact course your DiffEq final covers.
Proofs, combinatorics, probability distributions. Rebuilt from first principles for career-switchers.
Your practice exam breakdown
Calculus II · Integration Methods
Partial fractions improved 3 points after the annotated worked example on rational decomposition.
Who gets here with Proof
Maya T.
Mechanical Engineering, 2nd Year · DiffEq Final
“I was getting 52s on practice exams. After two weeks with Proof's annotated guides, I scored 89 on the actual final.”
Rohan A.
Data Science Bootcamp · Linear Algebra from Scratch
“The margin notes explained things my bootcamp instructor assumed I already knew. I didn't. Now I do.”
Simone B.
Pre-Med Freshman · Calculus I Retake
“Integration by parts finally clicked when I saw the geometric picture. It took 10 minutes. Not 10 weeks.”
Walk through a complete integration chapter with annotated notes, real-time problem solving, and Q&A. Limited to 40 students per session.
Reserve Your Seat — Free
Not ready? Download a Free Chapter
Integration Techniques — Chapter 3
24 pages · 18 worked examples · 6 margin-note annotations
The same chapter used in the live workshop. Integration by parts, u-substitution, and trig integrals — all annotated, all worked through completely.
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