# integration question? (1 Viewer)

#### nfreidman

##### New Member
how do you integrate 7^(2x+1) ?

#### SpiralFlex

##### Well-Known Member
$\bg_white \frac{1}{2\ln 7}* 7^{2x+1}+C$

[HR][/HR]

$\bg_white Let us consider, when differentiating some function, say -$

$\bg_white y=2^{2x+1}$

$\bg_white The result stems from,\; \frac{d}{dx}a^{bx+c} = (\ln a)*a^{bx+c}*b$

$\bg_white y'=\ln 2* 2^{2x+1}*2$

$\bg_white y'=2(\ln 2) 2^{2x+1}$

$\bg_white If we were to integrate that, we would sort of need to *knock out* the excess constants of (2ln2) to get back to our original function.$

$\bg_white The reverse process can be applied here, however when we reverse the result, we must do.$

$\bg_white \int a^{bx+c} \;dx=\frac{1}{b\ln a}*a^{bx+c}+C$

$\bg_white Hence we can apply it for this case.$

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#### barbernator

##### Active Member
replace 7 with e^ln(7).

integrate

#### Fus Ro Dah

##### Member
$\bg_white \frac{1}{2\ln 7}* 7^{2x+1}+C$
Correct, but maybe you should explain from where you acquired this answer, rather than just throwing it at nfreidman.

#### SpiralFlex

##### Well-Known Member
Correct, but maybe you should explain from where you acquired this answer, rather than just throwing it at nfreidman.
Am editing.

#### barbernator

##### Active Member
Correct, but maybe you should explain from where you acquired this answer, rather than just throwing it at nfreidman.
spiral knows his shit br8.

#### VJ30

##### Member
well u can use- (integral) a^x dx= a^x/lna +c but since there is a function in the power u can use substitution u=2x+1 and then go forward!

##### Banned
y= [e^ln(7)]^ (2x+1)

= e^[ (2x+1) ln(7) ]

Integrating

1/[2ln(7)] e^(2x+1)ln(7) ]

= 1/[2ln(7)] * y

= 1/ [2ln(7) ] 7^(2x+1)+C

#### Fus Ro Dah

##### Member
spiral knows his shit br8.
I am sure he does.

My point was that OP would have learnt better from an explanation, rather than just the final answer. The matter is not whether Spiralflex 'knows his shit' or not, but whether he could have explained it, which again I am confident he can.

#### SpiralFlex

##### Well-Known Member
You know me. Never leave stuff unexplained. I have a habit of typing the answer first then editing it.

#### barbernator

##### Active Member
I am sure he does.

My point was that OP would have learnt better from an explanation, rather than just the final answer. The matter is not whether Spiralflex 'knows his shit' or not, but whether he could have explained it, which again I am confident he can.
spiral always provides solutions, I should have said.

One thing he has left unexplained is his GF(real or imaginary)

#### iSplicer

##### Well-Known Member
replace 7 with e^ln(7).

integrate
+1

Best and simplest way to think about it.