Change of variable, trigonometry, cosine, integral.

[STEP II 1996 Question 4 (Pure)]

Arctan, logarithmic integration, substitution.

[STEP I 1996 Question 4 (Pure)]

Sine and modulus function, integration by parts.

[STEP I 1992 Question 3 (Pure)]

Integration by substitution, curve sketching, polynomial, distinct roots, inequality.

[STEP I 1990 Question 5 (Pure)]

Integration by substitution, trigonometry, monstrously hard.

[STEP II 1988 Question 7 (Pure)]

Integration by parts, trigonometry, substitution.

[STEP I 1988 Question 9 (Pure)]

Integration by substitution, trigonometric function, parameter.

[STEP II 1987 Question 6 (Pure)]

Integration by substitution, equivalent, 1/t, 1/x, trigonometry.

[STEP I 1987 Question 8 (Pure)]

Integer part, floor function, curve sketching, exponential function.

[STEP II Specimen Question 7 (Pure)]