Integrate

Question

sec^2x tan^2x?

Answer 1

Substitution method

ʃ sec²x tan²x dx

Let tanx = t

Differentiating with respst to x.

d/dx(tanx) = d/dx(t)

sec²x = dt/dx

sec²x dx = dt

Now the integral becomes

= ʃ t² dt

Apply the formula ʃ xⁿ = (x^{n + 1})/(n + 1) + C

= (t^{2 + 1} )/(2 + 1) + C

= (t³/3) + C

Back substitute t  = tanx.

ʃ sec²x tan²x dx = (tan³x)/3 + C.