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How to find integrals in this example: (intergral) 25 * (e^-0.2t) * dt
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A u-substitution would work. Let u = -0.2 t. So du = -0.2 dt. Or [1/(-0.2)] du = dt. Or -5 du = dt. So our original integral is equivalent to (integral) 25 * e^u * (-5) du. integral e^u du is just e^u + C. So (integral) 25 * e^u * (-5) du = -125 e^u + C. Since u = -0.2 t, we can express answer in terms of t, and we get -125 e^(-0.2 t) + C as our final answer.
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