Solve the trigonometric integral $\int\frac{1}{2}\cos\left(x^2\right)dx$

Find the integral

$\int cos\left(x^2\right)dx$

Find the integral

$\int\left(sin\left(x^2\right)\right)dx$

Find the integral

$\int\sin\left(x^2\right)\:dx$

Find the integral

$\int\left(cos\left(x^2\right)\right)dx$

Find the integral

$\int sin\left(x^2\right)dx$

Find the integral

$\int\left(sin\left(t^2\right)\right)dt$

Find the integral

$\int cos\left(x^3\right)dx$