I am trying to integrate this function: $\tan(x) \sqrt{1+\sec^4(x)}$. Please help me with this. Additionally, how do I confront all these problem in the future? Thank you.
Integrate $\tan(x)\sqrt{1+\sec^4(x)}$
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calculus
integration
indefinite-integrals
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0Do you intend $\sec^4(x)$ or $\sec{4x}$? – 2017-02-09
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0@Tim Thayer sec^4(x). the first one. I am sorry. I am new here I don't know how to superscript the number. – 2017-02-09
1 Answers
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Hint:
Just substitute $u = \sec^4 x +1$ to get $\frac {du}{dx} = 4\sec^4 x \tan x $. Then, we have, $$I= \int \tan x \sqrt {1+\sec^4 x}\mathrm {d}x $$ $$= \frac {1}{4} \int \frac {\sqrt {u}}{u-1} \mathrm {d}u $$
Hope you can take it from here.
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0Thank you very much. I can solve from there. – 2017-02-09
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0@UtsavBhattarai Happy it helped. – 2017-02-09