Edexcel IALMathematicsGeneral Applications5 Marks
Use the substitution u = sec(x) to show that ∫tan(x)secⁿ(x) dx = (secⁿ(x))/n + C for n ≠ 0.
Mark scheme
Marking points from the official mark scheme. The mark or mark type is shown in brackets.
- M1 for correctly finding du/dx or dx/du. (du/dx = sec(x)tan(x) or dx/du = 1/(sec(x)tan(x))).
- A1 for correctly expressing dx in terms of du: dx = du/(sec(x)tan(x)).
- M1 for substituting u and dx into the integral: ∫tan(x)uⁿ (du/(u tan(x))).
- A1 for simplifying the integral to ∫u^(n-1) du.
- A1 for correctly integrating and substituting back: (uⁿ)/n + C = (secⁿ(x))/n + C.
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