What is the integral of sin(2)(pix)cos(5)(pix) ?

The integral of sin(2)(pix)cos(5)(pix) is (pi^2)/3 sin(2)cos(5)x^3+C

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integral of sin(2)(pix)cos(5)(pix)

\int sin (2) (π x) cos (5) (π x) d x

\frac{π ^{2}}{3} sin (2) cos (5) x^{3} + C

Solution steps

\int sin (2) π x cos (5) π x d x

Take the constant out:

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

= sin (2) π cos (5) π \cdot \int xx d x

sin (2) π cos (5) π = π^{2} sin (2) cos (5)

= π^{2} sin (2) cos (5) \cdot \int xx d x

Simplify

xx : x^{2}

= π^{2} sin (2) cos (5) \cdot \int x^{2} d x

Apply the Power Rule

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

= π^{2} sin (2) cos (5) \frac{x ^{3}}{3}

Simplify

π^{2} sin (2) cos (5) \frac{x ^{3}}{3} : \frac{π ^{2}}{3} sin (2) cos (5) x^{3}

= \frac{π ^{2}}{3} sin (2) cos (5) x^{3}

Add a constant to the solution

= \frac{π ^{2}}{3} sin (2) cos (5) x^{3} + C

y^{^{''}} - 2 y^{^{'}} + 1 y = 0

\int \frac{sin ^{3} ( θ )}{cos ^{6} ( θ )} d θ

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

\frac{\partial}{\partial x} (x^{z} y^{1 - z})

- 3 e^{x + 4} + e^{3}

What is the integral of sin(2)(pix)cos(5)(pix) ?
The integral of sin(2)(pix)cos(5)(pix) is (pi^2)/3 sin(2)cos(5)x^3+C