Find the definite integral 1 inverted 4E ^ X / xdx under radical sign

Find the definite integral 1 inverted 4E ^ X / xdx under radical sign

If the title is:
∫ (1,4) [e ^ (root x) / root x] DX
Then you can:
The original formula = ∫ (1,4) [2 * e ^ (radical x)] d (radical x)
=2 * e ^ (radical x) | (1,4)
=2*e^2 - 2*e
=2e² - 2e

Definite integral of 1 / (1 + radical x)

OK, if I don't define the integral, let's take it in

What is the value of arctan (Tan θ)?

Let Tan θ = t
arctan(tanθ)=arctant=θ

Calculation of Tan and arctan~~~~~~~~~~~~~~~~~~~~~~~ tan(2arctan(2)) How to distribute the answer? Don't tell me about calculators~

Let Tan α = 2, then arctan2 = α
So the formula = tan2 α = 2tan α / [1 - (Tan α) ^ 2] = 2 * 2 / (1-2 ^ 2) = - 4 / 3

Ask arctan (1 / Tan (a)) why

=arctan(cota)
=arctan[tan(kπ+π/2-a)]
=kπ+π/2-a
Where - π / 2

What is the difference between arctan and Tan ^ (- 1)?

LS is not right. Arctan's domain is all real numbers
(1) Arctan is the inverse function of tan. In order to make the inverse function of Tan exist, the definition domain of Tan is limited to (- pi / 2, PI / 2), so the definition domain of arctan is the range of Tan (- inf, INF), and the range of arctan is (- pi / 2, PI / 2)
(2) Tan ^ (- 1) is 1 / Tan, where x which makes Tan (x) = 0 cannot be taken

Given that the root of the equation 1 + sin (θ - π) / 1 + cos [(π / 2) - θ] = Tan (θ + π) - sec θ holds, find the value range of θ The left side of the equal sign is all in the root sign,

√{1+sin( θ-π）/1+cos[(π/2)-θ ]}=tan(θ+π）-secθ
√[(1-sinθ)/(1+sinθ)]=tanθ-1/cosθ
(cosθ/2-sinθ/2)/(cosθ/2+sinθ/2)=(sinθ-1)/(cosθ/2-sinθ/2)(cosθ/2+sinθ/2)
(cosθ/2-sinθ/2)^2=sinθ-1
1-sinθ=sinθ-1
sinθ=1
θ=2kπ+π/2

SEC = 1 / cos, why sec45 = radical 2 and 1 / cos = 2 / Radix 2?

seca=1/cosa
1 / cos45 ° = 2 / radical 2 = (√ 2) 2 / √ 2 = √ 2
Yes, no mistakes

Evaluate cos [arcsin (- radical 3 / 2)] 3Q

Arcsin range is [- π / 2, π / 2]
Sin (- π / 3) = - radical 3 / 2
So the original formula = cos (- π / 3) = cos (π / 3) = 1 / 2

2 / 3 root sign 9x + 6 times root sign 4 / 4 x equals

Put forward 9 and 1 / 4, and then divide them into 2 times root sign x + 3 times root sign x = 5 times root sign X