find antiderivative

Question

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

Answer 1

Step 1:

The function is .

Anti derivative of the function is integration of the function.

Integrate on each side with respect to .

Step 2:

Consider  .

Rewrite the function as .

Power rule of integration: .

Integral formula: .

.

Step 3:

Consider  .

Integral formula: .

.

Step 4:

Consider .

.

Substitute the results of in .

Solution:

.