What is the integral of sec^2(θ)tan^6(θ) ?

The integral of sec^2(θ)tan^6(θ) is (tan^7(θ))/7+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of sec^2(θ)tan^6(θ)

\int sec^{2} (θ) tan^{6} (θ) d θ

\frac{tan ^{7} ( θ )}{7} + C

Solution steps

\int sec^{2} (θ) tan^{6} (θ) d θ

Rewrite using trig identities

= \int (1 + tan^{2} (θ)) tan^{6} (θ) d θ

Apply u-substitution

: \int u^{6} d u

= \int u^{6} d u

Apply the Power Rule

: \frac{u ^{7}}{7}

= \frac{u ^{7}}{7}

Substitute back

u = tan (θ)

= \frac{tan ^{7} ( θ )}{7}

Add a constant to the solution

= \frac{tan ^{7} ( θ )}{7} + C

e^{p} (p + p p)

\frac{\partial}{\partial x} (\frac{y}{1 + x ^{2} y ^{2}})

y^{^{'}} - a \cdot y + b = 0

y^{^{'}} = \frac{( e ^{(\frac{x}{3})} + y )}{2}

\frac{d}{d x} (- 4 sin (8 x))

What is the integral of sec^2(θ)tan^6(θ) ?
The integral of sec^2(θ)tan^6(θ) is (tan^7(θ))/7+C