∫ (e^x −(2x+3)^4 )^3 dx


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

$\int {(e^{x} - {(2 x + 3)}^{4})}^{3} d x$
Commented by kaivan.ahmadi last updated on 24/Jul/20

$\int (e^{3 x} - 3 e^{2 x} {(2 x + 3)}^{4} + 3 e^{x} {(2 x + 3)}^{8} - {(2 x + 3)}^{12}) d x =$ $\frac{1}{3} e^{3 x} - \frac{1}{26} {(2 x + 3)}^{13} - 3 \int e^{2 x} {(2 x + 3)}^{4} d x + 3 \int e^{x} {(2 x + 3)}^{8} d x =$ $w e m u s t f i n d t w o i n t e g r a l s . w e f i n d o n e o f$ $t h e m a n d s i m i l a r l y y o u c a n f i n d a n o t h e r .$
Commented by kaivan.ahmadi last updated on 24/Jul/20

Commented by kaivan.ahmadi last updated on 24/Jul/20

$\int e^{2 x} {(2 x + 3)}^{4} d x = 8 e^{2 x} {(2 x + 3)}^{3} - 24 e^{2 x} {(2 x + 3)}^{2 +}$ $48 e^{2 x} (2 x + 3) - 48 e^{2 x}$
Commented by malwaan last updated on 25/Jul/20

$sir a h m a d i$ $t h e f i r s t t e r m m u s t b e$ $\frac{1}{2} e^{2 x} {(2 x + 3)}^{4} . . .$ $a n d s o o n . . . .$
Commented by malwaan last updated on 25/Jul/20
$∫e^x (2x+3)^8 dx = e^x {(2x+3)^8 −16(2x+3)^7 +224(2x+3)^6 −2688(2x+3)^5 +26880(2x+3)^4 −215040(2x+3)^3 +860160(2x+3)^2 −1720320(2x+3) +3440640}$
$\int e^{x} {(2 x + 3)}^{8} d x = e^{x} {{(2 x + 3)}^{8}$ $- 16 {(2 x + 3)}^{7} + 224 {(2 x + 3)}^{6}$ $- 2688 {(2 x + 3)}^{5}$ $+ 26880 {(2 x + 3)}^{4}$ $- 215040 {(2 x + 3)}^{3}$ $+ 860160 {(2 x + 3)}^{2}$ $- 1720320 (2 x + 3)$ $+ 3440640}$
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