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online math integration calculator
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Integral Calculator • With Steps
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x^2 (e^(4x) + 3)
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I need help integrating by parts the below
Integral of x^2 (e^(4x) + 3)
2 answers
Lots of writing here, I suggest you look up the Tabular method
----- diff. -- integ
+ | ... x^2 .. e^4x + 3
- | ... 2x ... (1/4)e^(4x) + 3x
+ | ... 2 .... (1/16)e^(4x) + (3/2)x^2
- | ... 0 ... (1/64)e^(4x) + (1/2)x^3
∫( x^2 (e^(4x) + 3) )dx
= (x^2)((1/4)e^(4x) + 3x) - 2x((1/16)e^(4x) + (3/2)x^2) + 2((1/64)e^(4x) + (1/2)x^3)
= (1/4)e^(4x)(x^2) + 3x^3 - (1/8)x e^4x - 3x^3 + (1/32)e^(4x) + x^3
= (1/32)e^(4x) )(8x^2 - 4x + 1) + x^3
Here is a great video that explains this shortcut
https://www.youtube.com/watch?v=2I-_SV8cwsw&t=695s
----- diff. -- integ
+ | ... x^2 .. e^4x + 3
- | ... 2x ... (1/4)e^(4x) + 3x
+ | ... 2 .... (1/16)e^(4x) + (3/2)x^2
- | ... 0 ... (1/64)e^(4x) + (1/2)x^3
∫( x^2 (e^(4x) + 3) )dx
= (x^2)((1/4)e^(4x) + 3x) - 2x((1/16)e^(4x) + (3/2)x^2) + 2((1/64)e^(4x) + (1/2)x^3)
= (1/4)e^(4x)(x^2) + 3x^3 - (1/8)x e^4x - 3x^3 + (1/32)e^(4x) + x^3
= (1/32)e^(4x) )(8x^2 - 4x + 1) + x^3
Here is a great video that explains this shortcut
https://www.youtube.com/watch?v=2I-_SV8cwsw&t=695s
1 answer