Value of x³/x-1 \, dx is

Correct Answer is : x44+Cx^4/4 + C4x4+C

1/3 x³ + 1/2 x² + x + (x-1) + c

Correct Answer is : x44+Cx^4/4 + C4x4+C

Test Index

Integral Calculus

Question : 9 of 73

Marks: +1, -0

Value of

\int \frac{x^3}{x-1} \, dx

Solution:

Concept:

Use polynomial division to simplify the integrand, then integrate term by term.

Explanation:

Divide

x^3

x-1

x^3 = (x-1)(x^2 + x + 1) + 1

Thus,

\frac{x^3}{x-1} = x^2 + x + 1 + \frac{1}{x-1}

Integrate:

\int x^2 \, dx = \frac{x^3}{3}

\int x \, dx = \frac{x^2}{2}

\int 1 \, dx = x

\int \frac{1}{x-1} \, dx = \log|x-1|

Combine:

\int \frac{x^3}{x-1} \, dx = \frac{x^3}{3} + \frac{x^2}{2} + x + \log|x-1| + c

Answer:

Option A:

\frac{1}{3} x^3 + \frac{1}{2} x^2 + x + \log(x-1) + c

(with absolute value implied).

Go to Question:

Prev Question

Next Question