Question

integrate sec²x/√(tan²x+4) using substitution method​

Answer 1

Answer:

log | tanx + √(tan²x + 4) | + C₁

Step-by-step explanation:

Let tanx = t.

differentiate on both sides w.r.t to x.

dt/dx = sec²x.

dx = dt/sec²x.

Now integrating the function w.r.t x.

∫Sec²x / √(tan²x + 4 )

Put value of tanx = t and dx = dt/sec²x.

=∫Sec²x / √(t² + 4 ) * dt/sec²x.

= ∫dt/√(t² + 4 )

= ∫dt/√[(t)² + (2)²]  

But It is of form ∫dx/√x² + a² = log| x + √ x² + a² | + C₁

= log | t + √[(t)² + (2)² | + C₁

= log  | t + √(t² + 4) | + C₁

= log | tanx + √(tan²x + 4) | + C₁