∫tan³(θ)sec(θ) dθ + ∫tan⁵(θ)sec(θ) dθ
You asked:
Evaluate the expression: \(\int{{\tan\left( θ \right)}^{3} \cdot \sec\left( θ \right)}dθ + \int{{\tan\left( θ \right)}^{5} \cdot \sec\left( θ \right)}dθ\)
MathBot Answer:
\[\int{{\tan\left( θ \right)}^{3} \cdot \sec\left( θ \right)}dθ + \int{{\tan\left( θ \right)}^{5} \cdot \sec\left( θ \right)}dθ = C_{1} + C_{2} + \frac{1 - 3 \cos^{2}{\left(θ \right)}}{3 \cos^{3}{\left(θ \right)}} - \frac{- 15 \cos^{4}{\left(θ \right)} + 10 \cos^{2}{\left(θ \right)} - 3}{15 \cos^{5}{\left(θ \right)}}\]