What is the integral of 2/(5cos^2(x)) ?

The integral of 2/(5cos^2(x)) is 2/5 tan(x)+C

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integral of 2/(5cos^2(x))

\int \frac{2}{5 cos ^{2} ( x )} d x

\frac{2}{5} tan (x) + C

Solution steps

\int \frac{2}{5 cos ^{2} ( x )} d x

Take the constant out:

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

= \frac{2}{5} \cdot \int \frac{1}{cos ^{2} ( x )} d x

Use the common integral:

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

= \frac{2}{5} tan (x)

Add a constant to the solution

= \frac{2}{5} tan (x) + C

\int sec (2 x) tan^{3} (2 x) d x

e^{\frac{x ^{2}}{2}}

\int_{0}^{\frac{π}{8}} sin^{2} (2 x) d x

sin (x) cos (x)

\int x^{3} (x^{4} + 3)^{2} d x

What is the integral of 2/(5cos^2(x)) ?
The integral of 2/(5cos^2(x)) is 2/5 tan(x)+C