Numerical Value Questions

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Try the first 5 questions

1.
If integral x^2 * e^(2x) dx = e^(2x)(ax^2 + bx + c) + K, find the value of 4a + 2b + c.
2.
If 1/((x+1)(x+2)(x+3)) = A/(x+1) + B/(x+2) + C/(x+3), then A + B + C equals:
3.
If integral sin^4(x) dx = (3x/8) - (sin 2x)/4 + (sin 4x)/32 + C, find the coefficient of x in the result.
4.
integral dx/(x^2 - 6x + 13) = (1/a)*arctan((x-3)/a) + C. Find a.
5.
If integral cos^3(x)/sin^2(x) dx = f(sin x) + C where f(t) = -1/t + t, find f(1/2). Give the answer as a decimal.

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