Integration by DD

Calculus Level 1

Integrate using any type of integration.

-4ln(x+4) +C x-4ln(x+4) +C ln(x+4) +C 74 +C

Dylan Scupin-Dursema by Dylan Scupin-Dursema , 29, USA

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2 solutions

Caleb Townsend
Mar 12, 2015

Let u = x + 4. u = x + 4. Then d x = d u dx = du and ∫ x x + 4 d x = ∫ u − 4 u d u = ∫ d u − ∫ 4 u d u = u − 4 ln ⁡ ( u ) + C 0 = x + 4 − 4 ln ⁡ ( x + 4 ) + C 0 \int \frac{x}{x+4} dx = \int \frac{u - 4}{u} du \\ = \int du - \int \frac{4}{u} du \\ = u - 4\ln(u) + C_0 \\ = x + 4 - 4\ln(x + 4) + C_0 C 0 C_0 is an arbitrary constant, so let C = C 0 + 4. C = C_0 + 4. ∫ x x + 4 d x = x − 4 ln ⁡ ( x + 4 ) + C \int \frac{x}{x+4} dx = \boxed{x - 4\ln (x+4) + C}

5 Helpful 0 Interesting 0 Brilliant 0 Confused

I added +4 to the numerator, and also subtracted 4. Then it becomes (x+4)/(x+4) -4/(x+4)... I have a date with LaTex over spring break... Thanks Caleb!

Dylan Scupin-Dursema - 6 years, 3 months ago
Ahmed Essam
Mar 15, 2015

2 Helpful 0 Interesting 0 Brilliant 0 Confused

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