Make the u-substitution 1– u? 1+ u? to convert the integrand to a rational function of u, and then evaluate the integral. If you have a CAS, use it to evaluate the integral (no substitution), and then confirm that the results are 2u - dx 1+ u? sin x cos x and du 1+ u2' equivalent. 1 dx 4 sin x – 3 cos x -

Q: Find tan-1 x2 -dx using integration by parts.

A: Integral by parts

Q: | (cos c+ 1) dc;let x be constant

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Q: Integral: Evaluate -2 sin 2x xp= V9+ cos² 2x

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Q: Evaluate the definite integral two ways: first by a u-substitution in the definite integral and then…

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Q: 6z* cos (r*) dr-

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Q: sin x+3 cosr dx. Determine the following rational function 1+cosx

A: We have to first do partial fraction of the given expression.

Q: [3x² csc²(x)dx

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Q: 1 sin x + 2 cos x + 3

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Q: sin x-1 x+cos x -dx

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Q: sin(2x) cos(2x) dx 1+ cos(4x)

A: To evaluate: The integration of ∫sin2x·cos 2x1+cos 4xdx. Formula used: Trigonometric relation: 1+cos…