Evaluate the indefinite integral using recognition method. a) fxsin (x²)dx b) x²(x³ + 5)'dx c) (3x - 2)20 dx

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A: Let's find given integration by using given substitution.

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Q: QUESTION 2 a) Evaluate the integral | dx (x-5) +5 b) Show that 5+4x - x² = 9-(x-2) by completing the…

A: (a). From the given problem: I=∫5x-52+5dx   ...1 Let, u=x-5So,ddxu=ddxx-5dudx=1-0du=dx

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A: Perform integration

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Q: 2. Use Theorem 4 to evaluate (3x +2x2) dx

A: Given ∫01 (3x+2x2)We know that ∫xn=xn+1n+1+C

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Q: Evaluate the integral: x³ 4x² + 13x + 1 1 5x³x x2 - 4x + 13 dx

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