Use a u-substitution to rewrite the indefinite integral in terms of u and then evaluate. Give exact values only, no decimals. ∫(2)/(1+(7x+9)^2dx=∫g(u)du.

Question

u=?

du=? dx

g(u)=?

∫g(u)du=?+C

∫(2)/(1+(7x+9)^2dx=? +C

Answer 1

Because:

It's pretty straight forward to say:

let u = 7x + 9

du = 7dx or dx = du/7

Then the integral becomes:

or 2/7∫1/(1 + u²)du = 2/7arctan(u) = 2/7arctan(7x + 9) + C