What is the integral of xsin(s) ?

The integral of xsin(s) is 1/2 x^2sin(s)+C

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integral of xsin(s)

\int x sin (s) d x

\frac{1}{2} x^{2} sin (s) + C

Solution steps

\int x sin (s) d x

Take the constant out:

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

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

Apply the Power Rule

: \frac{x ^{2}}{2}

= sin (s) \frac{x ^{2}}{2}

Simplify

sin (s) \frac{x ^{2}}{2} : \frac{1}{2} x^{2} sin (s)

= \frac{1}{2} x^{2} sin (s)

Add a constant to the solution

= \frac{1}{2} x^{2} sin (s) + C

y = (7) (6^{x - 8})

x^{2} \frac{d y}{d x} + 4 x y - e^{x} = 0

(2 y - 8 x^{2}) d x + x d y = 0

\frac{d}{d x} (e^{x \cdot s i n (x)})

x \to 2 + lim (\frac{1}{x - 2})