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

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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

Apply the Power Rule

= \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

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