What is the integral from x to 2x of yzcos(x^5) ?

The integral from x to 2x of yzcos(x^5) is cos(x^5)y(2x^2-(x^2)/2)

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integral from x to 2x of yzcos(x^5)

\int_{x}^{2 x} yz cos (x^{5}) d z

cos (x^{5}) y (2 x^{2} - \frac{x ^{2}}{2})

Solution steps

\int_{x}^{2 x} yz cos (x^{5}) d z

Take the constant out:

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

= cos (x^{5}) y \cdot \int_{x}^{2 x} z d z

Apply the Power Rule

: [\frac{z ^{2}}{2}]_{x}^{2 x}

= cos (x^{5}) y [\frac{z ^{2}}{2}]_{x}^{2 x}

Compute the boundaries:

2 x^{2} - \frac{x ^{2}}{2}

= cos (x^{5}) y (2 x^{2} - \frac{x ^{2}}{2})

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What is the integral from x to 2x of yzcos(x^5) ?
The integral from x to 2x of yzcos(x^5) is cos(x^5)y(2x^2-(x^2)/2)