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1
Let u=x2+1\text{Let } u = x^2 + 1

Choose inner function

2
du=2x dxdu = 2x\,dx

Differentiate both sides

3
∫u3 du=u44+C\int u^3\,du = \frac{u^4}{4} + C

Integrate with respect to u

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Quadratic formula
x=−b±b2−4ac2ax = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
Euler's identity
eiπ+1=0e^{i\pi} + 1 = 0
Maxwell's equation
∇×E=−∂B∂t\nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}}{\partial t}
Schr\"odinger equation
iℏ∂∂t∣Ψ⟩=H^∣Ψ⟩i\hbar \frac{\partial}{\partial t}|\Psi\rangle = \hat{H}|\Psi\rangle

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Extracted 4 problems

Integral calculus — u-substitution, integration by parts...

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Session: U-Substitution12 min
7:48 / 12:00
0.5x1x2x4x
Tutor explains u-substitution concept
Student asks about inner function
Tutor shows differentiation step
Practice problem assigned

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