What is the integral of t^3e^{sin(t^4)}cos(t^4) ?

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

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integral of t^3e^{sin(t^4)}cos(t^4)

\int t^{3} e^{s i n (t^{4})} cos (t^{4}) d t

\frac{1}{4} e^{s i n (t^{4})} + C

Solution steps

\int t^{3} e^{s i n (t^{4})} cos (t^{4}) d t

Apply u-substitution

: \int \frac{1}{4} d u

= \int \frac{1}{4} d u

Integral of a constant:

\int a d x = a x

= \frac{1}{4} u

Substitute back

u = e^{s i n (t^{4})}

= \frac{1}{4} e^{s i n (t^{4})}

Add a constant to the solution

= \frac{1}{4} e^{s i n (t^{4})} + C

n = 0 \sum \infty 0. 9^{2 n}

cos^{2} (x) sin (x) y^{^{'}} + cos^{3} (x) y = 1

2 t \frac{d y}{d t} = 8 y

\frac{\partial}{\partial x} (x e^{6 y})

\frac{\partial}{\partial x} (\frac{x ^{\frac{3}{2}}}{3})

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