Question Number 104928 by bobhans last updated on 24/Jul/20

∫ (e^x −(2x+3)^4 )^3 dx

Commented bykaivan.ahmadi last updated on 24/Jul/20

∫(e^(3x) −3e^(2x) (2x+3)^4 +3e^x (2x+3)^8 −(2x+3)^(12) )dx= (1/3)e^(3x) −(1/(26))(2x+3)^(13) −3∫e^(2x) (2x+3)^4 dx+3∫e^x (2x+3)^8 dx= we must find two integrals.we find one of them and similarly you can find another.

Commented bykaivan.ahmadi last updated on 24/Jul/20

Commented bykaivan.ahmadi last updated on 24/Jul/20

∫e^(2x) (2x+3)^4 dx=8e^(2x) (2x+3)^3 −24e^(2x) (2x+3)^(2+) 48e^(2x) (2x+3)−48e^(2x)

Commented bymalwaan last updated on 25/Jul/20

sir ahmadi the first term must be (1/2) e^(2x) (2x + 3 )^4 ... and so on ....

Commented bymalwaan last updated on 25/Jul/20

∫e^x (2x+3)^8 dx = e^x {(2x+3)^8 −16(2x+3)^7 +224(2x+3)^6 −2688(2x+3)^5 +26880(2x+3)^4 −215040(2x+3)^3 +860160(2x+3)^2 −1720320(2x+3) +3440640}