What is the integral of ((5x)/(2y)-sec^2(x)) ?

The integral of ((5x)/(2y)-sec^2(x)) is (5x^2)/(4y)-tan(x)+C

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integral of ((5x)/(2y)-sec^2(x))

\int (\frac{5 x}{2 y} - sec^{2} (x)) d x

\frac{5 x ^{2}}{4 y} - tan (x) + C

Solution steps

\int \frac{5 x}{2 y} - sec^{2} (x) d x

Apply the Sum Rule:

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

= \int \frac{5 x}{2 y} d x - \int sec^{2} (x) d x

\int \frac{5 x}{2 y} d x = \frac{5 x ^{2}}{4 y}

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

= \frac{5 x ^{2}}{4 y} - tan (x)

Add a constant to the solution

= \frac{5 x ^{2}}{4 y} - tan (x) + C

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What is the integral of ((5x)/(2y)-sec^2(x)) ?
The integral of ((5x)/(2y)-sec^2(x)) is (5x^2)/(4y)-tan(x)+C