Integrate using partial fraction decomposition. int (1)/(3x^(3)-8x^(2)+5x)dx (4)/(5)ln(5-3x)-ln(1-x)+(ln(x))/(5)+C (1)/(4)ln(4-5x)-(ln(x))/(4)+C (3)/(10)ln(5-3x)-(1)/(2)ln(1-x)+(ln(x))/(5)+C (1)/(7)ln(5-3x)-(1)/(7)ln(1-2x)+C 3((3)/(10)ln(5-3x)-(1)/(2)ln(1-x)+(ln(x))/(5))+C Integrate using partial fraction decomposition. 1 dx 3 x3-8 2+5 x 4 1n(x) 1n5-3x-1n1-x+ +C 5 1n(x) 1n(4 -5x) +C 4 4 0 11 ln(x) 1n1-x+ +c 2 5 10 1I 1 1n(5 - 3 x) - 1n1-2x+C 7 7 3/ 1n(x) 1n(5-3x)- 1n1-x+ 10 2
Added by Jaime L.
Close
Step 1
Step 1: Factor the denominator of the integrand: 3x^3 - 8x^2 + 5x = x(3x^2 - 8x + 5) = x(3x - 5)(x - 1) Show more…
Show all steps
Your feedback will help us improve your experience
Naresh Bagrecha and 62 other Calculus 1 / AB educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Integrate (Partial Fractions)
Naresh B.
Integrate. (Partial Fractions).
Darshan M.
Use the method of partial fraction decomposition to perform the required integration. $\int \frac{5 x+7}{x^{2}+4 x+4} d x$
Techniques of Integration
Integration of Rational Functions Using Partial Fractions
Recommended Textbooks
Calculus: Early Transcendentals
Thomas Calculus
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD