D (∫ Sint / TDT) / DX (upper limit 2x, lower limit 2)

D (∫ Sint / TDT) / DX (upper limit 2x, lower limit 2)

d[∫(sint/t)dt]/dx=sin(2x)/(2x)*(2x)'=sin(2x)/x

Finding definite integral ∫ (1 ~ √ 3) x / √ x ^ 2 + 1 DX

The original formula = ∫ tank * sectdt (let x = tank and simplify)
=∫d(sect)
=sec(π/3)-sec(π/4)
=2-√2

Indefinite integral of (x ^ 3sinx ^ 2) / (x ^ 4 + 2x ^ 2 + 1)

Should the problem be to find definite integral? If we can't find definite integral, the original function can't be expressed by finite elementary function, but definite integral can be found
Let f (x) = (x ^ 3sinx ^ 2) / (x ^ 4 + 2x ^ 2 + 1)
=(x^3sinx^2)/(x^2+1)^2
f(-x)=-f(x)
Therefore, the integrand is an odd function. If the integrand interval is symmetric about the origin, then the definite integral is directly equal to 0, and there is no need to find the indefinite integral