∫ 1/x^2＋4x＋5 dx＝? How to calculate the specific steps!

∫ 1/x^2＋4x＋5 dx＝? How to calculate the specific steps!

∫dx/(x^2+4x+5)
=∫dx/[(x+2)^2+1]
=arctan(x+2) +C

How do you calculate the integral of ∫ (x ^ 2) exp (- x ^ 2) DX, from negative infinity to positive infinity

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You know the normal distribution
f(x)=[1/√(2pi)]*exp(-x^2)
EX=0 DX=1
Ex ^ 2 = DX + (Ex) ^ 2 = 1 = ∫ x ^ 2F (x) DX from negative infinity to positive infinity
therefore
∫x^2*[1/√(2pi)]*exp(-x^2)dx=1
∫(x^2)exp(-x^2)dx=√(2pi）

The generalized integral ∫ exp (- x ^ 2) DX, from negative infinity to positive infinity. It seems that the original function can't be solved. How to calculate it?

Instead of using the original function calculation and using the double integral calculation, there are many on the network. If you only need the value, you can find the Gaussian integral. The value is equal to 2pi, and PI here is the PI

Calculate the integral (x ^ 2 / x ^ 4 + x ^ 2 + 1) DX. The integral interval is negative infinity to positive infinity

Have you studied complex functions? The best way is to use the residue in the complex variable function to calculate. The contour of the integral selects the line segment of [- R, R] on the real axis and the line segment with R as the radius, 0

Calculate [1 / (1 + x ^ 2)] DX - ∞

[1/(1+x^2)]dx
=Arctanx|negative infinity to positive infinity
=(pai)/2-[-(pai)/2]
=pai

Calculate the generalized integral ∫ (1,2) DX / [x (x ^ 2-1) ^ (1 / 2)]

Let x = sect
Original formula = ∫ (0, π / 3) DT = π / 3