What is the integral of 9xcos(x) ?

The integral of 9xcos(x) is 9(xsin(x)+cos(x))+C

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integral of 9xcos(x)

\int 9 x cos (x) d x

9 (x sin (x) + cos (x)) + C

Solution steps

\int 9 x cos (x) d x

Take the constant out:

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

= 9 \cdot \int x cos (x) d x

Apply Integration By Parts

: x sin (x) - \int sin (x) d x

= 9 (x sin (x) - \int sin (x) d x)

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

= 9 (x sin (x) - (- cos (x)))

Simplify

= 9 (x sin (x) + cos (x))

Add a constant to the solution

= 9 (x sin (x) + cos (x)) + C

\frac{d y}{d x} = \frac{1}{y}

f (x) = x^{3} (x - 8)^{2}

\frac{d y}{d x} = e^{2 y} sin (3 x)

f (x) = \frac{7}{x}, at x = 1

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

What is the integral of 9xcos(x) ?
The integral of 9xcos(x) is 9(xsin(x)+cos(x))+C