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    Calculus - Antiderivates & Integrals

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    Find antiderivatives and Integrals. ...

    [See the attached questions file.]

    © BrainMass Inc. brainmass.com October 9, 2019, 9:38 pm ad1c9bdddf
    https://brainmass.com/math/integrals/calculus-antiderivates-integrals-192574

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    (2) ∫ 5x dx = 5 ∫ x dx = (5/2) x^2 + C
    (4) ∫ (t^2 + t) dt = ∫ t^2 dt + ∫ t dt
    = (1/3) t^3 + (1/2) t^2 + C
    (6) ∫ √z dz = ∫ z^(1/2) dz = (2/3) z^(3/2) + C
    (8) ∫ dt/t^2 = ∫ t^-2 dt = -1/t + C
    (10) ∫ e^z dz = e^z + C
    (12) Given integral = 2 ∫ t^2 dt + 3 ∫ t^3 dt + 4 ∫ t^4 dt
    = (2/3) t^3 + (3/4) t^4 + (4/5) t^5 + C
    (14) Given integral = ∫ y^4 dy + ∫ (1/y)dy
    = (1/5) y^5 + ln y + C
    (16) ∫ (t^2 + 1)dt/t = ...

    Solution Summary

    Neat, step-by-step solution to the given antiderivatives is provided.

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