Line integral $F(x,y,z) = \left( 2xyz + sin(x)\right)\mathbf i + x^2z \mathbf j +x^2 y \mathbf k $ Let $F(x,y,z) = \left( 2xyz + sin(x)\right)\mathbf i + x^2z \mathbf j +$ $x^2 y \mathbf k $. Evaluate
$$ \int_C F \cdot ds$$
where C is the parametrized curve $ c(t) = \left(cos^5(t),sin^3(t),t^4\right), 0\le t \le \pi $

I tried to calculate this line integral by calculating the derivative of the c and dot product of the F and c' as the integrand. But the calculation is so complicated, so I think there might be much easier way to do this.
Observe that

$$\text{curl}\,F:=\begin{vmatrix}i&amp;j&amp;\;\;k\\\frac\partial{\partial x}&amp;\frac\partial{\partial y}&amp;\;\;\frac\partial{\partial z}\\2xyz+\sin x&amp;x^z&amp;\;\;x^2y\end{vmatrix}=0$$
Observe that

$$\text{curl}\,F:=\begin{vmatrix}i&amp;j&amp;\;\;k\\\frac\partial{\partial x}&amp;\frac\partial{\partial y}&amp;\;\;\frac\partial{\partial z}\\2xyz+\sin x&amp;x^z&amp;\;\;x^2y\end{vmatrix}=0$$