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
RS
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