If ∫x3e5xdx=e5x54(f(x))+c, then fx=

∫x3e5xdxFind derivatives of x3 continuously x3 3x2 6x 6→1 next find integration of e5x continuously e5x5 e5x25 e5x125 e5x625 →2 Now multiply 1& 2 and change the sign for 2nd 4th ......terms ∴∫x3e5xdx =x3e5x5-3x2e5x25+6x e5x125-6e5x625 =e5x54x3.53-75x2+30x-6

If ∫x3e5xdx=e5x54(f(x))+c, then fx=

∫x3e5xdxFind derivatives of x3 continuously x3 3x2 6x 6→1 next find integration of e5x continuously e5x5 e5x25 e5x125 e5x625 →2 Now multiply 1& 2 and change the sign for 2nd 4th ......terms ∴∫x3e5xdx =x3e5x5-3x2e5x25+6x e5x125-6e5x625 =e5x54x3.53-75x2+30x-6

AI Mentor

Check Your IQ

Free Expert Demo

Try Test

Courses

Dropper NEET Course Dropper JEE Course Class - 12 NEET Course Class - 12 JEE Course Class - 11 NEET Course Class - 11 JEE Course Class - 10 Foundation NEET Course Class - 10 Foundation JEE Course Class - 10 CBSE Course Class - 9 Foundation NEET Course Class - 9 Foundation JEE Course Class -9 CBSE Course Class - 8 CBSE Course Class - 7 CBSE Course Class - 6 CBSE Course

Offline Centres

If $\int x^{3} e^{5 x} d x = \frac{e^{5 x}}{5^{4}} (f (x)) + c,$ then $f (x) =$

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

$\frac{x^{3}}{5} - \frac{3 x^{2}}{5^{2}} + \frac{6 x}{5^{3}} - \frac{6}{5^{4}}$

$5^{2} x^{3} - 15^{2} x^{2} + 30 x - 6$

$5 x^{3} - 5^{2} x^{2} + 5^{2} x - 6$

$5^{3} x^{3} - 75 x^{2} + 30 x - 6$

answer is D.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

$\int x^{3} e^{5 x} d x$

$F i n d d e r i v a t i v e s o f x^{3} c o n t i n u o u s l y x^{3} 3 x^{2} 6 x 6 \to (1) n e x t f i n d i n t e g r a t i o n o f e^{5 x} c o n t i n u o u s l y \frac{e^{5 x}}{5} \frac{e^{5 x}}{25} \frac{e^{5 x}}{125} \frac{e^{5 x}}{625} \to (2) N o w m u l t i p l y 1 & 2 a n d c h a n g e t h e s i g n f o r 2 n d 4 t h . . . . . . t e r m s ∴ \int x^{3} e^{5 x} d x = x^{3} \frac{e^{5 x}}{5} - 3 x^{2} \frac{e^{5 x}}{25} + 6 x \frac{e^{5 x}}{125} - \frac{6 e^{5 x}}{625} = \frac{e^{5 x}}{5^{4}} [x^{3} . 5^{3} - 75 x^{2} + 30 x - 6]$