What is the integral of 5xsin(yz) ?

The integral of 5xsin(yz) is 5/2 x^2sin(yz)+C

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integral of 5xsin(yz)

\int 5 x sin (yz) d x

\frac{5}{2} x^{2} sin (yz) + C

Solution steps

\int 5 x sin (yz) d x

Take the constant out:

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

= 5 sin (yz) \cdot \int x d x

Apply the Power Rule

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

= 5 sin (yz) \frac{x ^{2}}{2}

Simplify

5 sin (yz) \frac{x ^{2}}{2} : \frac{5}{2} x^{2} sin (yz)

= \frac{5}{2} x^{2} sin (yz)

Add a constant to the solution

= \frac{5}{2} x^{2} sin (yz) + C

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What is the integral of 5xsin(yz) ?
The integral of 5xsin(yz) is 5/2 x^2sin(yz)+C