Question

2. Calculate. (a) \int \frac{1}{x^2 + 7x + 6} dx. (b) \int \frac{x^5}{(x - 2)^2} dx. (c) \int \frac{1}{x^2 - 6x + 13} dx. (d) \int \frac{x}{x^2 - 6x + 13} dx. (e) \int \frac{1}{(x^2 - 2x + 2)^2} dx. (f) \int \frac{x}{(x^2 - 2x + 2)^2} dx. (g) \int \frac{x^4}{x^5 - 1} dx. (h) \int \frac{x^5 + x^2}{x^4 - 1} dx. (i) \int \frac{x^4}{x^3 + x^2 - 2x} dx. (j) \int \frac{1}{(x - 1)(x^2 + 1)^2} dx.

          2. Calculate.

(a) \int \frac{1}{x^2 + 7x + 6} dx.
(b) \int \frac{x^5}{(x - 2)^2} dx.
(c) \int \frac{1}{x^2 - 6x + 13} dx.
(d) \int \frac{x}{x^2 - 6x + 13} dx.
(e) \int \frac{1}{(x^2 - 2x + 2)^2} dx.
(f) \int \frac{x}{(x^2 - 2x + 2)^2} dx.
(g) \int \frac{x^4}{x^5 - 1} dx.
(h) \int \frac{x^5 + x^2}{x^4 - 1} dx.
(i) \int \frac{x^4}{x^3 + x^2 - 2x} dx.
(j) \int \frac{1}{(x - 1)(x^2 + 1)^2} dx.

2. Calculate.

(a) ∫(1)/(x^2 + 7x + 6) dx.
(b) ∫(x^5)/((x - 2)^2) dx.
(c) ∫(1)/(x^2 - 6x + 13) dx.
(d) ∫(x)/(x^2 - 6x + 13) dx.
(e) ∫(1)/((x^2 - 2x + 2)^2) dx.
(f) ∫(x)/((x^2 - 2x + 2)^2) dx.
(g) ∫(x^4)/(x^5 - 1) dx.
(h) ∫(x^5 + x^2)/(x^4 - 1) dx.
(i) ∫(x^4)/(x^3 + x^2 - 2x) dx.
(j) ∫(1)/((x - 1)(x^2 + 1)^2) dx.

Added by Tommy G.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Ma. Theresa Alin

08/17/2022

Step 1

Step 1: For (a) \int \frac{1}{x^{2}+7x+6}dx, we can factor the denominator to get \int \frac{1}{(x+1)(x+6)}dx. Show more…

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Thanks for your feedback!

Calculate. (a) int (1)/(x^(2)+7x+6)dx. (f) int (x)/((x^(2)-2x+2)^(2))dx. (b) int (x^(5))/((x-2)^(2))dx. (g) int (x)/(x^(4)-1)dx. (c) int (1)/(x^(2)-6x+13)dx. (h) int (x^(5)+x^(2))/(x^(4)-1)dx. (d) int (x)/(x^(2)-6x+13)dx. (i) int (x^(4))/(x^(3)+x^(2)-2x)dx. (e) int (1)/((x^(2)-2x+2)^(2))dx. (j) int (1)/((x-1)(x^(2)+1)^(2))dx. 2. Calculate. a) 1 dx 2 + 7 + 6 2+2 b) gf (c) (h) x x4 (p dx 2 6x+ 13 i Z- z + g e) i 1)(2 + 1)2