How do I integrate tan^2 x?
Firstly, use the trigonometric formula tan2x = sec2x - 1, which you can easily derive from sin2x + cos2x =1, by dividing both sides by cos2x and re-arranging. Now, you should remember that differentiating tan x gives sec2x. Therefore, the opposite is true for integration, integrating sec2x gives tan x. Also, differentiating x gives 1, hence, integrating 1 gives x. With this knowledge you can express tan2x as sec2x - 1 and integrate it to give tan x -x +C.
JC
Related Maths A Level answers
All answers ▸A particle, P, moves along the x-axis. The displacement, x metres, of P is given by 0.5t^2(t^2 - 2t + 1), when is P instantaneously at rest
sin(x)/(cos(x)+1) + cos(x)/(sin(x)+1) = 1
Find the roots of x^3 + 4x^2 - 5x
Simplify (5-2√3)/(√3-1) giving your answer in the form p +q√3, where p and q are rational numbers