Question

(integral) e^3x dx

A. e^3x+C
B. 1/3e^3x+C
C. e^4x+C
D. 1/4e^4x+C

Evaluate (integral) dx/(Square root 9-8x-x^2)

A. sin^-1(x+4/5)+C
B. sin^-1(x-4/5)+C
C. Ln(Square root 9-8x-x^2)+C
D. Ln(-8-2x)+C

Answer 1

if u = 3x you have integral e^u du/3, so (B)

since 9-8x-x^2 = 25 - (x+4)^2, and integral du/sqrt(a^2-u^2) = arcsin(u/a), you have arcsin u/5, so (A)