What is the integral of 16xsin(x) ?

The integral of 16xsin(x) is 16(-xcos(x)+sin(x))+C

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integral of 16xsin(x)

\int 16 x sin (x) d x

16 (- x cos (x) + sin (x)) + C

Solution steps

\int 16 x sin (x) d x

Take the constant out:

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

= 16 \cdot \int x sin (x) d x

Apply Integration By Parts

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

= 16 (- x cos (x) - \int - cos (x) d x)

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

= 16 (- x cos (x) - (- sin (x)))

Simplify

= 16 (- x cos (x) + sin (x))

Add a constant to the solution

= 16 (- x cos (x) + sin (x)) + C

\frac{1 + x}{1 - x}

\int_{0}^{e} ln (x) d x

\int (1 + e)^{x} d x

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

\int x^{3} (1 - x^{4})^{5} d x

What is the integral of 16xsin(x) ?
The integral of 16xsin(x) is 16(-xcos(x)+sin(x))+C