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

The integral of-2sec^2(x) is -2tan(x)+C

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integral of-2sec^2(x)

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

- 2 tan (x) + C

Solution steps

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

Take the constant out:

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

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

Use the common integral:

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

= - 2 tan (x)

Add a constant to the solution

= - 2 tan (x) + C

\frac{d y}{d x} + 5 y = 10

f (x) = x^{2} - 18 x - 4

\int (2 x - x - \frac{9}{x ^{2}}) d x

y^{^{''}} - 4 y^{^{'}} + 4 y = t^{3} e^{2 t}, y (0) = 0, y^{^{'}} (0) = 0

f (x) = cot (x)