What is the integral of (1+tan(θ))^5sec^2(θ) ?

The integral of (1+tan(θ))^5sec^2(θ) is ((1+tan(θ))^6)/6+C

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integral of (1+tan(θ))^5sec^2(θ)

\int (1 + tan (θ))^{5} sec^{2} (θ) d θ

\frac{( 1 + tan ( θ ) ) ^{6}}{6} + C

Solution steps

\int (1 + tan (θ))^{5} sec^{2} (θ) d θ

Apply u-substitution

= \int u^{5} d u

Apply the Power Rule

= \frac{u ^{6}}{6}

Substitute back

u = 1 + tan (θ)

= \frac{( 1 + tan ( θ ) ) ^{6}}{6}

Add a constant to the solution

= \frac{( 1 + tan ( θ ) ) ^{6}}{6} + C

What is the integral of (1+tan(θ))^5sec^2(θ) ?
The integral of (1+tan(θ))^5sec^2(θ) is ((1+tan(θ))^6)/6+C