What is the integral of xcos(3x^2) ?

The integral of xcos(3x^2) is 1/6 sin(3x^2)+C

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integral of xcos(3x^2)

\int x cos (3 x^{2}) d x

\frac{1}{6} sin (3 x^{2}) + C

Solution steps

\int x cos (3 x^{2}) d x

Apply u-substitution

: \int \frac{cos ( u )}{6} d u

= \int \frac{cos ( u )}{6} d u

Take the constant out:

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

= \frac{1}{6} \cdot \int cos (u) d u

Use the common integral:

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

= \frac{1}{6} sin (u)

Substitute back

u = 3 x^{2}

= \frac{1}{6} sin (3 x^{2})

Add a constant to the solution

= \frac{1}{6} sin (3 x^{2}) + C

x \to 0 lim (\frac{1 + x}{x})

y = (5 x^{2} + x) (x - x^{2})

y = - x^{2} + 2 x + 6, y = - x + 6

\int x^{2} + sin (x) + 1 d x

x \to - \infty lim (\frac{8 x ^{3}}{9 x ^{4}})

What is the integral of xcos(3x^2) ?
The integral of xcos(3x^2) is 1/6 sin(3x^2)+C