integrals
- Thread starter Anny_LL
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Hints for #6
2sin(x)-cos(x)
= √5 * [2/√5 * sin(x) - 1/√5 * cos(x)] ..... let cos(Θ) = 2/√5 & sin(Θ) = 1/√5
= √5 * sin (x - Θ) and continue.....
HallsofIvy
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For (1) you have \(\displaystyle \int 2^x\sqrt{4x+ 2^{x+ 1}+ 5} dx\) (Though you forgot the "dx". That's important.)
That is extremely difficult and may, in fact, not have an "elementary" integral. But if you meant
\(\displaystyle \int 2^x\sqrt{4^x+ 2^{x+ 1}+ 5}dx\)
that's much easier. \(\displaystyle 4^x= (2^2)^x= (2^x)^2\) and \(\displaystyle 2^{x+ 1}=2(2^x)\). Use the substitution \(\displaystyle u= 2^x\)
That is extremely difficult and may, in fact, not have an "elementary" integral. But if you meant
\(\displaystyle \int 2^x\sqrt{4^x+ 2^{x+ 1}+ 5}dx\)
that's much easier. \(\displaystyle 4^x= (2^2)^x= (2^x)^2\) and \(\displaystyle 2^{x+ 1}=2(2^x)\). Use the substitution \(\displaystyle u= 2^x\)