What is the integral of sin(-1(x)) ?

The integral of sin(-1(x)) is cos(x)+C

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integral of sin(-1(x))

\int sin (- 1 (x)) d x

cos (x) + C

Solution steps

\int sin (- 1 \cdot x) d x

Simplify

sin (- 1 \cdot x) : - sin (x)

= \int - sin (x) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - \int sin (x) d x

Use the common integral:

\int sin (x) d x = - cos (x)

= - (- cos (x))

Simplify

= cos (x)

Add a constant to the solution

= cos (x) + C

x \to 0 - lim (\frac{sec ( x )}{x})

y^{^{''}} + 6 y^{^{'}} + 6 y = 0, y (0) = 1, y^{^{'}} (0) = 2

\frac{d}{d x} ((x - 1)^{2} + y^{2})

f (x) = x^{3} + 2 x

2 x^{3} + 4 x^{2} - x + 2