- #1

FaraDazed

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## Homework Statement

Integrate the following indefinite integrals

A:[itex]\int e^x (x^2+1) dx[/itex]

B:[itex]\int e^x cos(3x+2) dx[/itex]

## Homework Equations

[itex]\int u dv = uv - \int v du [/itex]

## The Attempt at a Solution

Part A: I have done the following but when I use an integration calculator online its not what I have (although I suppose there's a few ways of doing it)

[tex]

let \, u=x^2 +1 \,\, ∴ \, du=2x \\

let \, dv=e^x \,\, ∴ \, v=e^x \\

\\

∴e^x(x^2+1)-\int e^x 2x \, dx \\

[/tex]

Then doing another by parts on that integral

[tex]

let \, u=2x \,\, ∴ \, du=2 \\

let \, dv=e^x \,\, ∴ \, v=e^x \\

\\

2xe^x-2\int e^x \, dx = 2xe^x-2e^x + C

[/tex]

Then plugging that into the first bit I get

[tex]

e^x(x^2+1)-2xe^x-2e^x + C

[/tex]For Part B:

I am really confused as it doesn't look like a u-sub problem and no matter which way around I set the variables to do a by parts problem, the resulting integral is no easier to solve than the original so any hints on where to start with that one would be much appreciated.

Thanks :)

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