_ ^ (x + 3) ( x^2 + 6x + 10) ^9 ;dx equals - Vidyadip

MCQ

$\int_{}^{} {(x + 3){{({x^2} + 6x + 10)}^9}\;dx} $ equals

✓
$\frac{1}{{20}}{({x^2} + 6x + 10)^{10}} + c$
B
$\frac{1}{{20}}{(x + 3)^2}{({x^2} + 6x + 10)^{10}} + c$
C
$\frac{1}{{16}}{({x^2} + 6x + 10)^8} + c$
D
$\frac{1}{{38}}{(x + 3)^{19}} + \frac{1}{2}(x + 3) + c$

✓

Answer

Correct option: A.

$\frac{1}{{20}}{({x^2} + 6x + 10)^{10}} + c$

a
(a)$\int_{}^{} {(x + 3){{({x^2} + 6x + 10)}^9}dx} $
$ = \frac{1}{2}\int_{}^{} {(2x + 6){{({x^2} + 6x + 10)}^2}dx} $
$ = \frac{1}{2}\frac{{{{({x^2} + 6x + 10)}^{10}}}}{{10}} + c$$ = \frac{1}{{20}}{({x^2} + 6x + 10)^{10}} + c$.

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