What is the integral of xsec^2(y) ?

The integral of xsec^2(y) is xtan(y)+C

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integral of xsec^2(y)

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

x tan (y) + C

Solution steps

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

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

Use the common integral:

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

= x tan (y)

Add a constant to the solution

= x tan (y) + C