What is the integral of sin(5)(t)cos(4)(t) ?

The integral of sin(5)(t)cos(4)(t) is 1/3 sin(5)cos(4)t^3+C

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integral of sin(5)(t)cos(4)(t)

\int sin (5) (t) cos (4) (t) d t

\frac{1}{3} sin (5) cos (4) t^{3} + C

Solution steps

\int sin (5) t cos (4) t d t

Take the constant out:

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

= sin (5) cos (4) \cdot \int tt d t

Simplify

tt : t^{2}

= sin (5) cos (4) \cdot \int t^{2} d t

Apply the Power Rule

: \frac{t ^{3}}{3}

= sin (5) cos (4) \frac{t ^{3}}{3}

Simplify

sin (5) cos (4) \frac{t ^{3}}{3} : \frac{1}{3} sin (5) cos (4) t^{3}

= \frac{1}{3} sin (5) cos (4) t^{3}

Add a constant to the solution

= \frac{1}{3} sin (5) cos (4) t^{3} + C

x \to \infty lim (6 x^{3})

2 π r - π r^{2}

n = 0 \sum \infty (\frac{2 x}{3})^{n}

\int \frac{4 e ^{x}}{e ^{2 x} + 2 e ^{x} + 1} d x

\frac{\partial}{\partial x} (x e^{5 x y})

What is the integral of sin(5)(t)cos(4)(t) ?
The integral of sin(5)(t)cos(4)(t) is 1/3 sin(5)cos(4)t^3+C