What is the integral of xcos(5x^2) ?

The integral of xcos(5x^2) is 1/10 sin(5x^2)+C

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integral of xcos(5x^2)

\int x cos (5 x^{2}) d x

\frac{1}{10} sin (5 x^{2}) + C

Solution steps

\int x cos (5 x^{2}) d x

Apply u-substitution

: \int \frac{cos ( u )}{10} d u

= \int \frac{cos ( u )}{10} d u

Take the constant out:

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

= \frac{1}{10} \cdot \int cos (u) d u

Use the common integral:

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

= \frac{1}{10} sin (u)

Substitute back

u = 5 x^{2}

= \frac{1}{10} sin (5 x^{2})

Add a constant to the solution

= \frac{1}{10} sin (5 x^{2}) + C

x \to 2 lim (\frac{4 x}{x - 4})

\frac{d}{d x} (\frac{x + 2}{2 - x})

\frac{\partial}{\partial k} (ln (sin (\frac{x}{k})))

\int \frac{x ^{2}}{4 x ^{3} + 7} d x

\frac{d}{d x} (\frac{1}{3} tan^{3} (\frac{1}{x}))

What is the integral of xcos(5x^2) ?
The integral of xcos(5x^2) is 1/10 sin(5x^2)+C