Question

Find the following indefinite integrals. Use C as your constant of integration. (a) ?(4x³ + 3x² + 2x + 5)dx = x^4+x^3+x^2+5x+C (b) ?(x + 5)²dx = (x+5)^3/3+C (c) ?(a · x² + b · x)dx = 1/3(ax^3)+1/2bx^2+C

          Find the following indefinite integrals. Use C as your constant of integration.
(a) ?(4x³ + 3x² + 2x + 5)dx = x^4+x^3+x^2+5x+C
(b) ?(x + 5)²dx = (x+5)^3/3+C
(c) ?(a · x² + b · x)dx = 1/3(ax^3)+1/2bx^2+C

Added by Laurie C.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Adi S

06/12/2023

Step 1

We can integrate each term separately: ∫(4x^3)dx = x^4 + C_1 ∫(3x^2)dx = x^3 + C_2 ∫(2x)dx = x^2 + C_3 ∫(S)dx = Sx + C_4 Now, we can add all the integrals together and combine the constants: ∫(4x^3 + 3x^2 + 2x + S)dx = x^4 + x^3 + x^2 + Sx + (C_1 + C_2 + C_3 + Show more…

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(a) ∫(4x^3 + 3x^2 + 2x + 5)dx = x^4 + x^3 + x^2 + 5x + C (b) ∫(x + 5)^2dx = (1/3)(x + 5)^3 + C (c) ∫(a * x^2 + b * x)dx = (1/3)(a * x^3) + (1/2)(b * x^2) + C