What is the integral of-6sin(x) ?

The integral of-6sin(x) is 6cos(x)+C

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integral of-6sin(x)

\int - 6 sin (x) d x

6 cos (x) + C

Solution steps

\int - 6 sin (x) d x

Take the constant out:

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

= - 6 \cdot \int sin (x) d x

Use the common integral:

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

= - 6 (- cos (x))

Simplify

= 6 cos (x)

Add a constant to the solution

= 6 cos (x) + C

\frac{d y}{d x} - \frac{4}{x} y = y^{5} \frac{1}{x ^{8}}

\int 3 x (3 - x^{- 8}) d x

\frac{d}{d x} (6 cos^{4} (3 x + 2))

x^{2} + 1

y^{^{''}} - 3 y^{^{'}} + 2 y = 0, y (0) = 1, y^{^{'}} (0) = - 1