What is the integral of asin(x) ?

The integral of asin(x) is -acos(x)+C

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integral of asin(x)

\int a sin (x) d x

- a cos (x) + C

Solution steps

\int a sin (x) d x

Take the constant out:

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

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

Use the common integral:

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

= a (- cos (x))

Simplify

= - a cos (x)

Add a constant to the solution

= - a cos (x) + C

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

y^{2} = 4 x, y = 2 x + 4

y = 3 - x, y = 9 - x^{2}

x \to 5 + lim (\frac{∣ 5 - x ∣}{5 - x})

y^{^{''}} + 9 y = - 30 sin (3 t)