What is the integral of sin(x)sec^3(x) ?

The integral of sin(x)sec^3(x) is (tan^2(x))/2+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of sin(x)sec^3(x)

\int sin (x) sec^{3} (x) d x

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

Solution steps

\int sin (x) sec^{3} (x) d x

Rewrite using trig identities

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

Apply u-substitution

: \int u d u

= \int u d u

Apply the Power Rule

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

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

Substitute back

u = tan (x)

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

Add a constant to the solution

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

x y^{2} + 3 y^{2} - x^{2} \frac{d y}{d x} = 0

\int_{2}^{6} x d x

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

\frac{\partial}{\partial x} (x \cdot e^{x y})

x = y^{2} - 1, x = y

What is the integral of sin(x)sec^3(x) ?
The integral of sin(x)sec^3(x) is (tan^2(x))/2+C