Calculus

# Integration of Trigonometric Functions

Find the indefinite integral $\int{11\tan^6 x \sec^4 x}dx.$

Find the indefinite integral $\displaystyle \int{23\tan^5 \theta \sec^7 \theta}d\theta.$

If $f(\theta) = \int \frac{\sin^3 \theta - \cos^3 \theta}{\sin \theta - \cos \theta} d\theta + \int (1- \sin \theta \cos \theta) d\theta$ and $f(0) = 10,$ what is the value of $f(30)?$

Evaluate $\int_{-4}^{7}\left( \sin x+4\cos x \right)^2 dx + \int_{-4}^{7}\left( 4\sin x-\cos x \right)^2 dx.$

What is the value of $N = \int_0^{\pi} \sin x\ dx$?

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