What is the integral of t^2sin(β)t ?

The integral of t^2sin(β)t is 1/4 t^4sin(β)+C

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integral of t^2sin(β)t

\int t^{2} sin (β) t d t

\frac{1}{4} t^{4} sin (β) + C

Solution steps

\int t^{2} sin (β) t d t

Take the constant out:

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

= sin (β) \cdot \int t t^{2} d t

Simplify

t t^{2} : t^{3}

= sin (β) \cdot \int t^{3} d t

Apply the Power Rule

: \frac{t ^{4}}{4}

= sin (β) \frac{t ^{4}}{4}

Simplify

sin (β) \frac{t ^{4}}{4} : \frac{1}{4} t^{4} sin (β)

= \frac{1}{4} t^{4} sin (β)

Add a constant to the solution

= \frac{1}{4} t^{4} sin (β) + C

\int csc (x) cot (x) d x

f (x) = - 8 x sin (4 x^{2} + 1)

\frac{d}{d x} (- f (x) sin (x) + g (x) cos (x))

\int \frac{x + 3}{5 - 4 x - x ^{2}} d x

What is the integral of t^2sin(β)t ?
The integral of t^2sin(β)t is 1/4 t^4sin(β)+C