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

f (x) = x^{2} - 6 x, at x = 7

\int - 2 x + 1 d x

f (x) = \frac{- 8 x + 2}{3 x + 5}

\int e^{- \frac{x}{2}} sin (2 x) d x

x \to 0 + lim ((1 + x)^{l n (x)})