Find the indefinite integral. [ Hint: Use u = x 2 + 8 and integral u n du = 1 /n

Question

Find the indefinite integral. [Hint: Use u = x2 + 8 and integral undu = 1 /n+1 un + 1 + C (n 1).] (Use C for the constant of integration.)

integral (x2 + 8)92x dx

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Find the indefinite integral by the substitution method or state that it cannot be found by our substitution formulas. (If it cannot be found by substitution, enter IMPOSSIBLE. Use C for the constant of integration. Remember to use ln(|u|) where appropriate.)

integral dx / 3 + 2x

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(Use C for the constant of integration.)

un + 1 + C (n 1).]

(Use C for the constant of integration.)

integral dx / 3 + 2x

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Explanation / Answer

(x2 + 8)92x dx

put x2 + 8 = u

==> 2x dx = du

==> (x2 + 8)92x dx = u9 du

==> u10/10 + c

==> (x2 + 8)10/10 + c

2) 1/(3 +2x) dx

put 3 +2x = u

==> 2dx = du

==> dx = du/2

==> 1/(3 +2x) dx = 1/u du/2

==> (1/2)(ln u) + c

==> (1/2)(ln (3 +2x)) + c

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