What is the integral of xcos(7x^2) ?

The integral of xcos(7x^2) is 1/14 sin(7x^2)+C

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integral of xcos(7x^2)

\int x cos (7 x^{2}) d x

\frac{1}{14} sin (7 x^{2}) + C

Solution steps

\int x cos (7 x^{2}) d x

Apply u-substitution

: \int \frac{cos ( u )}{14} d u

= \int \frac{cos ( u )}{14} d u

Take the constant out:

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

= \frac{1}{14} \cdot \int cos (u) d u

Use the common integral:

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

= \frac{1}{14} sin (u)

Substitute back

u = 7 x^{2}

= \frac{1}{14} sin (7 x^{2})

Add a constant to the solution

= \frac{1}{14} sin (7 x^{2}) + C

\frac{d}{d x} (\frac{x}{x})

\int_{0}^{1} 3 + 9 x^{2} d x

\frac{d}{d x} (\frac{e ^{x}}{9 x})

\int_{0}^{1} (2 x - 3) (5 x + 1) d x

\int \frac{1}{2} sin (x) d x

What is the integral of xcos(7x^2) ?
The integral of xcos(7x^2) is 1/14 sin(7x^2)+C