Question

evaluate the indefinite integral
∫(x-2)e^(x^2-4x-3)dx

Answer 1

Let \(u=x^2-4x-3\)

Answer 2

i dont understand how to do the u sustitution

Answer 3

see if this helps
https://www.khanacademy.org/math/integral-calculus/integration-techniques/u_substitution/v/u-substitution

Answer 4

@ganeshie8 is this correct?

Answer 5

what about \(u = (x-2)^2\)

Answer 6

differentiate your answer and see if you get back the integrand

Answer 7

\[\dfrac{d}{dx} \left(\color{red}{\dfrac{1}{2}e^{x^2-4x-3}+C}\right) = ?\]

Answer 8

xe^(x^2)-4

Answer 9

du is 2x-4.... what do i do with the (X-2) then?

Answer 10

2x -4 = 2( x -2 )

Answer 11

2e^(x^2-4x-3)+C

Answer 12

u= x^2-4x-3
du = (2x -4) dx
du = 2( x-2) dx
du /2 = (x-2) dx

Answer 13

$$
\large \int (x-2) e^{x^2-4x-3} dx
\\ = \large \int e^{x^2-4x-3} (x-2)dx
\\ = \large \int e^{u}~ \frac{du}{2} =
\frac 1 2 \large \int e^{u}~ du
$$

Answer 14

1/2 e^(x^2-4x-3) + C

Answer 15

thats correct