Solve the differential equation: dy/dx = tan^3(x)sec^2(x)

dy/dx = tan³(x)sec²(x)

Integrate both sides ==> ∫dy= ∫ tan³(x)sec²(x) dx

Use the substitution u=tan(x)

And by differentiation du/dx = sec²(x) , which leads to dx = du/sec²(x)

==> and subbing dx into the equation leads to the simplification of y = ∫ u³ du

Integrate with respect to u to get y = u⁴/4 + c

Then sub u back into the equation to find y = tan⁴(x) + c