What is the integral of 17xsin(17x^2) ?

The integral of 17xsin(17x^2) is -1/2 cos(17x^2)+C

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integral of 17xsin(17x^2)

\int 17 x sin (17 x^{2}) d x

- \frac{1}{2} cos (17 x^{2}) + C

Solution steps

\int 17 x sin (17 x^{2}) d x

Take the constant out:

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

= 17 \cdot \int x sin (17 x^{2}) d x

Apply u-substitution

: \int \frac{sin ( u )}{34} d u

= 17 \cdot \int \frac{sin ( u )}{34} d u

Take the constant out:

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

= 17 \cdot \frac{1}{34} \cdot \int sin (u) d u

Use the common integral:

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

= 17 \cdot \frac{1}{34} (- cos (u))

Substitute back

u = 17 x^{2}

= 17 \cdot \frac{1}{34} (- cos (17 x^{2}))

Simplify

17 \cdot \frac{1}{34} (- cos (17 x^{2})) : - \frac{1}{2} cos (17 x^{2})

= - \frac{1}{2} cos (17 x^{2})

Add a constant to the solution

= - \frac{1}{2} cos (17 x^{2}) + C

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What is the integral of 17xsin(17x^2) ?
The integral of 17xsin(17x^2) is -1/2 cos(17x^2)+C