Techniques of  Integration - General

Techniques of  Integration

H2 Math

International Baccalaureate Higher Level Mathematics

IB HL Math

ACJC Tutorial Question 17

Evaluate \$\\displaystyle\int \\frac{1}{1 + \\cos x} \\, \mathrm{d}x\$\n\nUsing \$\\cos 2\\theta = 2\\cos^2\\theta - 1\$, so \$\\cos x = 2\\cos^2\\frac{x}{2} - 1\$\n\n\$1 + \\cos x = 1 + 2\\cos^2\\frac{x}{2} - 1 = 2\\cos^2\\frac{x}{2}\$

\$\\displaystyle\int \\frac{1}{2\\cos^2\\frac{x}{2}} \\, \mathrm{d}x = \\frac{1}{2} \\displaystyle\int \\sec^2\\frac{x}{2} \\, \mathrm{d}x\$\n\n\$= \\frac{1}{2} \\cdot \\frac{\\tan\\frac{x}{2}}{\\frac{1}{2}} + C\$\n\n\$= \\tan\\frac{x}{2} + C\$

ACJC Tutorial Question 17

ACJC Tutorial Question 17

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