Question

## 20 POINTS ##

Solve the give question in pic
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Answer 1

Answer:

√2 √tanx ( 5 + tan²x)/5 + C

Step-by-step explanation:

sin2x = 2 tanx cos²x

∫dx/cos³x√sin2x = ∫dx/cos⁴x√tanx

√tanx = t²

Differentiating , and substituting we get

∫sec²x( 1 + tan²x) / √2tanx = ∫(2t*(1+t⁴)/t√2

Integrating and substituting for t = √ tanx

we get

√2 (5√tanx + (√tanx)⁵) / 5

Answer 2

Step-by-step explanation:

answer is in the attachment