The correct option is A #10; e^x(2x^3 6x^2+7x+3)+c #10; ∫ e^x(2x^3 5x+10)dx 2x^3 5x+10=(ax^3+bx^2+cx+d)+(3ax^2+2bx+c) a=2; nbsp; b+6= ...

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Integration by Parts

∫ ex2x3-5x+10...

Question

$\int e^{x} (2 x^{3} - 5 x + 10) d x =$

e^{x} (2 x^{3} - 6 x^{2} + 7 x + 3) + c

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e^{x} (2 x^{3} + 6 x^{2} - 7 x - 13) + c

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e^{x} (2 x^{3} - 6 x^{2} + 7 x - 13) + c

No worries! We‘ve got your back. Try BYJU‘S free classes today!

e^{x} (2 x^{3} + 6 x^{2} + 7 x + 13) + c

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Solution

The correct option is A $e^{x} (2 x^{3} - 6 x^{2} + 7 x + 3) + c$
$\int e^{x} (2 x^{3} - 5 x + 10) d x$
$2 x^{3} - 5 x + 10 = (a x^{3} + b x^{2} + c x + d) + (3 a x^{2} + 2 b x + c)$
$a = 2; b + 6 = 0 b = - 6; c + 2 b = - 5 c = 7; d + c = 10 d = 3$
$2 x^{3} - 5 x + 10 = (2 x^{3} - 6 x^{2} + 7 x + 3) + (6 x^{2} - 12 x + 7)$
$\int e^{x} (2 x^{3} - 5 x + 10) d x = \int e^{x} [(2 x^{3} - 6 x^{2} + 7 x + 3) + (6 x^{2} - 12 x + 7)] d x$
It is in the form of $\int e^{x} (f (x)) + f^{(} x)] d x = e^{x} f (x) + c$
$= e^{x} (2 x^{3} - 6 x^{2} + 7 x + 3) + c$

Suggest Corrections

Similar questions

6 x^{2} - 7 x - 13 = 0

Tick $(✓)$ the correct answer in each of the following:
$(2 x + 3) (3 x - 1) = ?$

(a) $(6 x^{2} + 8 x - 3)$
(b) $(6 x^{2} + 7 x - 3)$
(c) $6 x^{2} - 7 x - 3$
(d) $(6 x^{2} - 7 x + 3)$

6 x^{2} + 7 x - 3

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