Question

∫ (secxy + siny²) dx

Answer 1

$\int \sec(xy)dx+\int \sin{y^2}dx={\frac 1 y}\log(\sec(xy)+\tan(xy))+x\sin{y^2}+C$

reference for secant integral formula: https://ocw.mit.edu/courses/mathematics/18-01sc-single-variable-calculus-fall-2010/unit-4-techniques-of-integration/part-a-trigonometric-powers-trigonometric-substitution-and-completing-the-square/session-71-integrals-involving-secant-cosecant-and-cotangent/MIT18_01SCF10_Ses71c.pdf