How to find the integral of x 3^(x^2)

[intenzxboi]

Homework Statement

\int x 3^(x^2)

Homework Equations

integration by parts

The Attempt at a Solution

u= x dv= 3^(x^2)
du = 1 dx v=((3^(x^2))/ln 3 ) 2x + c ??

(x)((3^(x^2))/ln 3 ) 2x - \int ((3^(x^2))/ln 3 ) 2x dx

is this right??

 

[Unco]

Homework Statement

\int x 3^(x^2)

Homework Equations

integration by parts

The Attempt at a Solution

u= x dv= 3^(x^2)
du = 1 dx v=((3^(x^2))/ln 3 ) 2x + c ??

No: what do you get when you differentiate your v? 3^(x^2) doesn't have a nice integral.

Rather, you should recognise \int x3^{x^2} \, dx is built for a substitution: let u = x^2.

 

[intenzxboi]

so u=x^2
du = 2x

1/2 3^u du??

 

[Hitman2-2]

so u=x^2
du = 2x

1/2 3^u du??

do you mean

<br /> <br /> \frac{1}{2}\int 3^u du<br /> <br />

 

[intenzxboi]

are u sure about this.. people are telling me that i need to integrate by parts

 

[Hitman2-2]

are u sure about this.. people are telling me that i need to integrate by parts

Unco is correct: use the substitution

 

[HallsofIvy]

are u sure about this.. people are telling me that i need to integrate by parts

Then stop listening to those people!

 

[intenzxboi]

k gotcha. quick question what's the difference between integrating by parts and u substitution