Question

Evaluate the indefinite integral. (use c for the constant of integration.) tan6(θ) sec2(θ) dθ illustrate and check that your answer is reasonable by graphing both the function and its antiderivative (take c = 0). webassign plot webassign plot webassign plot webassign plot

Answer 1

$\displaystyle\int\tan^6\theta\sec^2\theta\,\mathrm d\theta$

$x=\tan\theta\implies\mathrm dx=\sec^2\theta\,\mathrm d\theta$

$\displaystyle\int x^6\,\mathrm dx=\dfrac{x^7}7+C$
$\implies\displaystyle\int\tan^6\theta\sec^2\theta\,\mathrm d\theta=\dfrac{\tan^7\theta}7+C$