What is the integral of 2/(cos(x))e^{2ln(cos(x))} ?

The integral of 2/(cos(x))e^{2ln(cos(x))} is 2sin(x)+C

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integral of 2/(cos(x))e^{2ln(cos(x))}

\int \frac{2}{cos ( x )} e^{2 l n (c o s (x))} d x

2 sin (x) + C

Solution steps

\int \frac{2}{cos ( x )} e^{2 l n (c o s (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 ( x )} e^{2 l n (c o s (x))} d x

Simplify

\frac{1}{cos ( x )} e^{2 l n (c o s (x))} : cos (x)

= 2 \cdot \int cos (x) d x

Use the common integral:

\int cos (x) d x = sin (x)

= 2 sin (x)

Add a constant to the solution

= 2 sin (x) + C

\int_{1}^{x} \frac{2}{x ^{3}} d x

y = \frac{x - 1}{x + 1}

\frac{d}{d x} (7 x^{- 6} - 5 x^{- 3})

\int cot^{7} (x) csc^{2} (x) d x

y = - 10

What is the integral of 2/(cos(x))e^{2ln(cos(x))} ?
The integral of 2/(cos(x))e^{2ln(cos(x))} is 2sin(x)+C