What is the integral of sec^2(θ)tan^7(θ) ?

The integral of sec^2(θ)tan^7(θ) is (tan^8(θ))/8+C

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integral of sec^2(θ)tan^7(θ)

\int sec^{2} (θ) tan^{7} (θ) d θ

\frac{tan ^{8} ( θ )}{8} + C

Solution steps

\int sec^{2} (θ) tan^{7} (θ) d θ

Rewrite using trig identities

= \int (1 + tan^{2} (θ)) tan^{7} (θ) d θ

Apply u-substitution

: \int u^{7} d u

= \int u^{7} d u

Apply the Power Rule

: \frac{u ^{8}}{8}

= \frac{u ^{8}}{8}

Substitute back

u = tan (θ)

= \frac{tan ^{8} ( θ )}{8}

Add a constant to the solution

= \frac{tan ^{8} ( θ )}{8} + C

x \to 2 lim (\frac{- 1}{( x + 2 )})

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

x \to 0 lim (16 - 7 x)

\int - cos (x) + C d x

\frac{d}{d t} (4 e^{- t})

What is the integral of sec^2(θ)tan^7(θ) ?
The integral of sec^2(θ)tan^7(θ) is (tan^8(θ))/8+C