check an answer?

**ally79** · August 28th 2008, 11:07 AM

Determine the integral:

6(3x+5)^11 dx

I got 6 (3x+5/36)^12 +C

A yay or Nay would be great if someone doesn't mind

**Moo** · August 28th 2008, 11:16 AM

Originally Posted by ally79

Determine the integral:

6(3x+5)^11 dx

I got 6 (3x+5/36)^12 +C

A yay or Nay would be great if someone doesn't mind

Erm.... does Ynay work ?

It's (6(3x+5)^12)/36 +C=((3x+5)^12)/6 +C, not what you've written

Try to figure it out. Putting parenthesis can sometimes help ! ^^

**Marine** · August 28th 2008, 11:20 AM

Hi!

You can proved it by yourself by differentiating it

or try the linear substitution

all the best, marine

**Prove It** · August 29th 2008, 04:21 AM

Originally Posted by ally79

Determine the integral:

6(3x+5)^11 dx

I got 6 (3x+5/36)^12 +C

A yay or Nay would be great if someone doesn't mind

$\int 6(3x+5)^{11} dx$

Let $u=3x+5$ and so $\frac{du}{dx}=3$

So $\int 6(3x+5)^{11} dx=2\int 3(3x+5)^{11} dx = 2\int u^{11} \frac{du}{dx} dx$
$= 2 \int u^{11}du = \frac{1}{6} u^{12} +C = \frac{1}{6}(3x+5)^{12}+C$

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