x*(sin(x))^2

Input

x sin^2(x)

Plot

Plot
Plot

Expanded trigonometric form

x/2 + 1/2 x sin^2(x) - 1/2 x cos^2(x)

Reduced trigonometric form

1/2 (x + x (-1) cos(2 x))

Alternate form

-1/4 e^(-2 i x) x - 1/4 e^(2 i x) x + x/2

Expanded cosine form

x - x cos^2(x)

Roots

x = π n, n element Z

Integer root

x = 0

Properties as a real function

Domain

R (all real numbers)

Range

R (all real numbers)

Surjectivity

surjective onto R

Parity

odd

Series expansion at x=0

x^3 - x^5/3 + (2 x^7)/45 + O(x^9) (Taylor series)
Big‐O notation »

Derivative

d/dx(x sin^2(x)) = sin(x) (sin(x) + 2 x cos(x))

Indefinite integral

integral x sin^2(x) dx = 1/8 (2 x (x - sin(2 x)) - cos(2 x)) + constant

Alternative representation

x sin^2(x) = x (1/csc(x))^2
x sin^2(x) = x cos^2(π/2 - x)
x sin^2(x) = x (-cos(π/2 + x))^2
More information »
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