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

The integral of (sqrt(tan(x)))/(cos^2(x)) is 2/3 tan^{3/2}(x)+C

Popular >

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

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

\frac{2}{3} tan^{\frac{3}{2}} (x) + C

Solution steps

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

Rewrite using trig identities

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

Apply u-substitution

: \int u d u

= \int u d u

Apply the Power Rule

: \frac{2}{3} u^{\frac{3}{2}}

= \frac{2}{3} u^{\frac{3}{2}}

Substitute back

u = tan (x)

= \frac{2}{3} tan^{\frac{3}{2}} (x)

Add a constant to the solution

= \frac{2}{3} tan^{\frac{3}{2}} (x) + C

x \to \frac{π}{2} lim (7 sin (x))

\int \frac{1}{x ^{- 1} + x ^{- 3}} d x

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

y = - 2 x^{3}, (2, - 16)

x \to 3 lim (\frac{∣ x + 3 ∣}{x - 3})

What is the integral of (sqrt(tan(x)))/(cos^2(x)) ?
The integral of (sqrt(tan(x)))/(cos^2(x)) is 2/3 tan^{3/2}(x)+C