Question

1. Evaluate the following integrals: a. $int_1^2 (ln x)^2 , dx$ b. $int an^4 x sec^6 x , dx$ c. $int x sqrt{25 - x^2} , dx$ d. $int frac{1}{x^2 sqrt{x^2 - 1}} , dx$ e. $int frac{dx}{(x-3)(x^2+1)}$

          1. Evaluate the following integrals:
a. $int_1^2 (ln x)^2 , dx$
b. $int 	an^4 x sec^6 x , dx$
c. $int x sqrt{25 - x^2} , dx$
d. $int frac{1}{x^2 sqrt{x^2 - 1}} , dx$
e. $int frac{dx}{(x-3)(x^2+1)}$

$1. Evaluate the following integrals: a. int1^2 (ln x)^2 , dx b. int an^4 x sec^6 x , dx c. int x sqrt25 - x^2 , dx d. int frac1x^2 sqrtx^2 - 1 , dx e. int fracdx(x-3)(x^2+1)$

Added by David L.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Drew Scalzo

Step 1

Use integration by parts with u = (ln x)^2, dv = dx. Then du = (2 ln x)/x dx and v = x. So I = [x (ln x)^2]_1^2 - ∫_1^2 x * (2 ln x)/x dx = [x (ln x)^2]_1^2 - 2 ∫_1^2 ln x dx. Show more…

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