Question

Evaluate the indefinite integral (1+x²) / (1+x)³dx

Answer 1

By using a substitution method, the indefinite integral ∫ x(x^2+1)^3 dx is evaluated to be 8(X^2+1)^4+C.

Step-by-step explanation:

We need to evaluate the indefinite integral ∫ x(x^2+1)^3 dx. The easiest way to tackle this integral is to use a substitution. Let u = x^2 + 1, which implies du = 2x dx.

Now, rewrite the integral in terms of u: ∫ ½(u^3) du. Integrate this expression to get ¼ u^4 + C, or ¼(x^2+1)^4 + C after back substitution.

Therefore, the correct answer is E) 8(X^2+1)^4+C.

completed question

Evaluate The Indefinite Integral. ∫X(X2+1)3dx A) 23(X2+1)2+C B) 4(X2+1)4+C C) 8x2(X2+1)4+C D) 3x(X2+1)2+C E) 8(X2+1)4+C