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Integration of Trigonometric Functions


Find the indefinite integral 11tan6xsec4xdx.\int{11\tan^6 x \sec^4 x}dx.

Find the indefinite integral 23tan5θsec7θdθ.\displaystyle \int{23\tan^5 \theta \sec^7 \theta}d\theta.

If f(θ)=sin3θcos3θsinθcosθdθ+(1sinθcosθ)dθ 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,f(0) = 10, what is the value of f(30)?f(30)?

Evaluate 47(sinx+4cosx)2dx+47(4sinxcosx)2dx. \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=0πsinx dxN = \int_0^{\pi} \sin x\ dx?


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