What is the integral of 6sin(x)+5 ?

The integral of 6sin(x)+5 is -6cos(x)+5x+C

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integral of 6sin(x)+5

\int 6 sin (x) + 5 d x

- 6 cos (x) + 5 x + C

Solution steps

\int 6 sin (x) + 5 d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 6 sin (x) d x + \int 5 d x

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

\int 5 d x = 5 x

= - 6 cos (x) + 5 x

Add a constant to the solution

= - 6 cos (x) + 5 x + C

\int x 2^{- x} d x

\frac{d y}{d x} = 3 x^{- 4}

\frac{d y}{d x} = 2 y - 3 y^{2}

\int_{0}^{2} cos (x^{2}) d x

\int x^{2} 6 x + 7 d x