Evaluate Integrate Integrate

Question

Evaluate       Integrate   Integrate

Robert · Accepted Answer

Evaluate    
√(1 + tan2x) = √sec2x = sec x
0∫π/4 sec x = ln |sec x + tan x|0π/4 = ln (√2 + 1)
Integrate   
Let sin x = p
=> cos x dx = dp
I = ∫2pdp =2p/ln 2 + k = 2sin x/ln 2 + k
Integrate  
Let 2x = p
· 2dx = dp
· dx = dp/2
I = ∫cosh p dp/2 = 0.5sinh p =0.5sinh 2x + k

Evaluate Integrate Integrate

Solution

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