What is the integral of 40sin((pix)/3)+50 ?

The integral of 40sin((pix)/3)+50 is -(120)/pi cos((pix)/3)+50x+C

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integral of 40sin((pix)/3)+50

\int 40 sin (\frac{π x}{3}) + 50 d x

- \frac{120}{π} cos (\frac{π x}{3}) + 50 x + C

Solution steps

\int 40 sin (\frac{π x}{3}) + 50 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 40 sin (\frac{π x}{3}) d x + \int 50 d x

\int 40 sin (\frac{π x}{3}) d x = - \frac{120}{π} cos (\frac{π x}{3})

\int 50 d x = 50 x

= - \frac{120}{π} cos (\frac{π x}{3}) + 50 x

Add a constant to the solution

= - \frac{120}{π} cos (\frac{π x}{3}) + 50 x + C

\int 3 + x \cdot (x + 1)^{2} d x

\frac{\partial}{\partial x} (x^{\frac{1}{2}})

\frac{d}{d x} (\frac{- 8 x}{x ^{2} + 1})

y = 3 x^{2} ln (x), y = 12 ln (x)

n = 1 \sum \infty 7 e^{- 2 n}

What is the integral of 40sin((pix)/3)+50 ?
The integral of 40sin((pix)/3)+50 is -(120)/pi cos((pix)/3)+50x+C