Keep in mind that the integral of ex = ex and 2x = ex / ln 2. You can then rewrite the exponent as u = 2x, convert dx to du, and from there it's pretty straightforward.
(I've left off the "+ C" part, because you should just know that.)
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-2x-2x-2x-2x-2=-32
Integral of 2x dx /(2x-2) Let 2x=u 2 dx = du dx = (1/2) du Integral of 2x dx /(2x-2) = Integral of (1/2) u du / (u-2) = Integral of 1/2 [ (u-2+2) / (u-2)] dx = Integral of 1/2 [ 1+ 2/(u-2)] dx = u/2 + (1/2) 2 ln(u-2) + C = u/2 + ln(u-2) + C = (2x/2) + ln(2x-2) + C = x + ln(2x-2) + C
Assuming that he quadratic is 2x^2 + x - 15, the quotient is 2x - 5.
4
To find the product of x squared and 2x squared, you multiply the coefficients (2 and 1) to get 2, and then add the exponents of x (2 and 2) to get x to the power of 4. Therefore, x squared times 2x squared is equal to 2x^4.