Find \(\int {(1 + {{\tan }^2}x){\text{d}}x} \).

Find \(\int {{{\sin }^2}x{\text{d}}x} \).

\(\int {(1 + {{\tan }^2}x){\text{d}}x}  = \int {{{\sec }^2}x{\text{d}}x = \tan x( + c)} \)     M1A1

[2 marks]

\(\int {{{\sin }^2}x{\text{d}}x}  = \int {\frac{{1 - \cos 2x}}{2}{\text{d}}x} \)     M1A1

\( = \frac{x}{2} - \frac{{\sin 2x}}{4}( + c)\)     A1

Note:     Allow integration by parts followed by trig identity.

Award M1 for parts, A1 for trig identity, A1 final answer.

[3 marks]

Total [5 marks]

Some correct answers but too many candidates had a poor approach and did not use the trig identity.

Same as (a).