What is the integral of sin(5)(t)cos(6)(t) ?

The integral of sin(5)(t)cos(6)(t) is 1/3 sin(5)cos(6)t^3+C

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integral of sin(5)(t)cos(6)(t)

\int sin (5) (t) cos (6) (t) d t

\frac{1}{3} sin (5) cos (6) t^{3} + C

Solution steps

\int sin (5) t cos (6) t d t

Take the constant out:

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

= sin (5) cos (6) \cdot \int tt d t

Simplify

tt : t^{2}

= sin (5) cos (6) \cdot \int t^{2} d t

Apply the Power Rule

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

= sin (5) cos (6) \frac{t ^{3}}{3}

Simplify

sin (5) cos (6) \frac{t ^{3}}{3} : \frac{1}{3} sin (5) cos (6) t^{3}

= \frac{1}{3} sin (5) cos (6) t^{3}

Add a constant to the solution

= \frac{1}{3} sin (5) cos (6) t^{3} + C

\int 3 x (x^{2} + 1)^{\frac{1}{2}} d x

\int (x^{\frac{1}{3}} - x^{\frac{2}{3}})^{2} d x

csc (x) cot (x)

y = (sin (3 x))^{l n (x)}

\frac{\partial}{\partial y} (ln (y^{x}))

What is the integral of sin(5)(t)cos(6)(t) ?
The integral of sin(5)(t)cos(6)(t) is 1/3 sin(5)cos(6)t^3+C