Advanced-Calculus-Evaluate-0-sec-4tan-2-5-d-L-rD-sE-GooD-LucK-

Question Number 118491 by Lordose last updated on 18/Oct/20

\dots ⧫ Advanced Calculus ⧫ \dots

Evaluate ::

Ω = \int_{0}^{\infty} \frac{\sec θ}{\sqrt{{4 \tan}^{2} θ + 5}} d θ

\dots ♠ L ϕ rD \emptyset sE ♠ \dots

\dots ♣ GooD LucK ♣

Answered by MJS_new last updated on 18/Oct/20

\int \frac{\sec θ}{\sqrt{5 + {4 \tan}^{2} θ}} d θ =

= sign (\cos x) \frac{\sqrt{5}}{5} \int \frac{d θ}{\sqrt{1 - \frac{1}{5} \sin^{2} θ}} =

= sign (\cos x) \frac{\sqrt{5}}{5} F (x ∣ \frac{1}{5}) + C

\Rightarrow Ω is not defined

[plot \frac{\sec θ}{\sqrt{5 + {4 \tan}^{2} θ}} and {you}^{'} ll see why]

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