Calculus - Antiderivates & Integrals
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Neat, step-by-step solution to the given antiderivatives is provided.
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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 = ...
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