What is the integral of 1/(sqrt(x)cos^2(\sqrt{x))} ?

The integral of 1/(sqrt(x)cos^2(\sqrt{x))} is 2tan(sqrt(x))+C

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integral of 1/(sqrt(x)cos^2(\sqrt{x))}

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

2 tan (x) + C

Solution steps

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

Apply u-substitution

: \int 2 sec^{2} (u) d u

= \int 2 sec^{2} (u) d u

Take the constant out:

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

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

Use the common integral:

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

= 2 tan (u)

Substitute back

u = x

= 2 tan (x)

Add a constant to the solution

= 2 tan (x) + C

\int \frac{1}{x + a ^{2} - x ^{2}} d x

\int \frac{ln ( x )}{1 + x} d x

\int x^{x} (ln (x) + 1) d x

\int \frac{x ^{2}}{( 1 - x ) ^{2021}} d x

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

What is the integral of 1/(sqrt(x)cos^2(\sqrt{x))} ?
The integral of 1/(sqrt(x)cos^2(\sqrt{x))} is 2tan(sqrt(x))+C