What is the integral of sec^2(θ)tan^{10}(θ) ?

The integral of sec^2(θ)tan^{10}(θ) is (tan^{11}(θ))/(11)+C

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integral of sec^2(θ)tan^{10}(θ)

\int sec^{2} (θ) tan^{10} (θ) d θ

\frac{tan ^{11} ( θ )}{11} + C

Solution steps

\int sec^{2} (θ) tan^{10} (θ) d θ

Rewrite using trig identities

= \int (1 + tan^{2} (θ)) tan^{10} (θ) d θ

Apply u-substitution

: \int u^{10} d u

= \int u^{10} d u

Apply the Power Rule

: \frac{u ^{11}}{11}

= \frac{u ^{11}}{11}

Substitute back

u = tan (θ)

= \frac{tan ^{11} ( θ )}{11}

Add a constant to the solution

= \frac{tan ^{11} ( θ )}{11} + C

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What is the integral of sec^2(θ)tan^{10}(θ) ?
The integral of sec^2(θ)tan^{10}(θ) is (tan^{11}(θ))/(11)+C