What is the integral of (1+4ytan^2(x)) ?

The integral of (1+4ytan^2(x)) is y+2y^2tan^2(x)+C

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integral of (1+4ytan^2(x))

\int (1 + 4 y tan^{2} (x)) d y

y + 2 y^{2} tan^{2} (x) + C

Solution steps

\int 1 + 4 y tan^{2} (x) d y

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 1 d y + \int 4 tan^{2} (x) y d y

\int 1 d y = y

\int 4 tan^{2} (x) y d y = 2 y^{2} tan^{2} (x)

= y + 2 y^{2} tan^{2} (x)

Add a constant to the solution

= y + 2 y^{2} tan^{2} (x) + C

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What is the integral of (1+4ytan^2(x)) ?
The integral of (1+4ytan^2(x)) is y+2y^2tan^2(x)+C