Strategies for u-Substitutions
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Problems 4
- Let I=∫0(2−1)/2dx(2x+1)x2+xI = \int_0^{(\sqrt{2} - 1)/2} \frac{dx}{(2x+1)\sqrt{x^2+x}}I=∫0(2−1)/2(2x+1)x2+xdx. Find π/I\pi/Iπ/I. Source: HMMT February 2002
- Evaluate ∫x2−12x−1 dx\int\frac{x^2-1}{\sqrt{2x-1}}\,dx∫2x−1x2−1dx Simplify your answer as much as possible.
- Compute ∫043x1+2x dx\int_0^4 \frac{3x}{\sqrt{1+2x}} \, dx∫041+2x3xdx.
- What is ∫2sin2(2x)cos(2x) dx\int 2 \sin^{2}(2x)\cos(2x) \, dx∫2sin2(2x)cos(2x)dx?