What is the integral of 10sin(x)2x ?

The integral of 10sin(x)2x is 20(-xcos(x)+sin(x))+C

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integral of 10sin(x)2x

\int 10 sin (x) 2 x d x

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

Solution steps

\int 10 sin (x) \cdot 2 x d x

Take the constant out:

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

= 10 \cdot 2 \cdot \int sin (x) x d x

Simplify

= 20 \cdot \int sin (x) x d x

Apply Integration By Parts

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

= 20 (- x cos (x) - \int - cos (x) d x)

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

= 20 (- x cos (x) - (- sin (x)))

Simplify

= 20 (- x cos (x) + sin (x))

Add a constant to the solution

= 20 (- x cos (x) + sin (x)) + C

\frac{d}{d x} (arcsec (x) + arccsc (x))

\frac{x}{x + 3}

y^{^{''}} - y = 0, y (0) = 1, y^{^{'}} (0) = 2

y = \frac{x ^{2} - 7 x + 2}{x - 2}

\int \frac{x}{( x ^{2} + 4 ) ^{\frac{3}{2}}} d x

What is the integral of 10sin(x)2x ?
The integral of 10sin(x)2x is 20(-xcos(x)+sin(x))+C