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This is the opposite of the derivative - and it's an integral part of Calculus. It's uses range from basic integrals to differential equations, with applications in Physics, Chemistry, and Economics.
Find the indefinite integral \(\int{11\tan^6 x \sec^4 x}dx.\)
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Find the indefinite integral \(\displaystyle \int{23\tan^5 \theta \sec^7 \theta}d\theta.\)
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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 \(f(30)?\)
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Evaluate \[ \int_{-4}^{7}\left( \sin x+4\cos x \right)^2 dx + \int_{-4}^{7}\left( 4\sin x-\cos x \right)^2 dx.\]
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What is the value of \(N = \int_0^{\pi} \sin x\ dx\)?
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