What is the integral of 7sin(2)(x)cos(3)(x) ?

The integral of 7sin(2)(x)cos(3)(x) is 7/3 sin(2)cos(3)x^3+C

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integral of 7sin(2)(x)cos(3)(x)

\int 7 sin (2) (x) cos (3) (x) d x

\frac{7}{3} sin (2) cos (3) x^{3} + C

Solution steps

\int 7 sin (2) x cos (3) x d x

Take the constant out:

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

= 7 sin (2) cos (3) \cdot \int xx d x

Simplify

xx : x^{2}

= 7 sin (2) cos (3) \cdot \int x^{2} d x

Apply the Power Rule

: \frac{x ^{3}}{3}

= 7 sin (2) cos (3) \frac{x ^{3}}{3}

Simplify

7 sin (2) cos (3) \frac{x ^{3}}{3} : \frac{7}{3} sin (2) cos (3) x^{3}

= \frac{7}{3} sin (2) cos (3) x^{3}

Add a constant to the solution

= \frac{7}{3} sin (2) cos (3) x^{3} + C

\frac{d}{d x} (\frac{x ^{2} ( x - 1 )}{( x + 1 ) ^{2}})

\frac{d ^{2}}{d x ^{2}} (\frac{7}{8 t ^{6}})

x \to 3 + lim (\frac{x ^{2} - 9}{x - 3})

\frac{x}{5 + x}

\frac{d}{d x} (5 sin (x))

What is the integral of 7sin(2)(x)cos(3)(x) ?
The integral of 7sin(2)(x)cos(3)(x) is 7/3 sin(2)cos(3)x^3+C