What is the integral of 2/(cos^2(x)) ?

The integral of 2/(cos^2(x)) is 2tan(x)+C

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integral of 2/(cos^2(x))

\int \frac{2}{cos ^{2} ( x )} d x

2 tan (x) + C

Solution steps

\int \frac{2}{cos ^{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 \frac{1}{cos ^{2} ( x )} d x

Use the common integral:

\int \frac{1}{cos ^{2} ( x )} d x = tan (x)

= 2 tan (x)

Add a constant to the solution

= 2 tan (x) + C

y^{^{''}} + y^{^{'}} - 6 y = 0, y (0) = 5, y^{^{'}} (0) = 2

\int 5 x^{2} + 3 x + 2 d x

\int_{0}^{5} (1 + 2 x^{3}) d x

\frac{d}{d x} ((\frac{x ^{2} + 2}{x ^{2} - 2})^{3})

\frac{\partial}{\partial x} (x arctan (x + 2 y))

What is the integral of 2/(cos^2(x)) ?
The integral of 2/(cos^2(x)) is 2tan(x)+C