"Evaluate the integral. ∫3x2+4x+4x3+xdx" solved and explained

Serotoninl7

Answered question

2021-11-09

Evaluate the integral.

\int 3 x^{2} + 4 x + \frac{4}{x^{3}} + x d x

Glenn Cooper

Beginner2021-11-10Added 12 answers

Step 1
Assume the given integral be I, Rewrite integral and simplify it

I = \int 3 x^{2} + 4 x + \frac{4}{x^{3}} + x d x

= \int 3 x^{2} d x + \int 4 x d x + \int \frac{4}{x^{3}} d x + \int x d x

= 3 \int x^{2} d x + 4 \int x d x + 4 \int x^{- 3} d x + \int x d x

Step 2
Integrate it by using:

\int x^{n} d x = \frac{x^{n + 1}}{n + 1} + C

I = 3 \frac{x^{3}}{3} + 4 \frac{x^{2}}{2} + 4 \frac{x^{- 3 + 1}}{- 3 + 1} + \frac{x^{2}}{2} + C

I = x^{3} + 2 x^{2} - \frac{2}{x^{2}} + \frac{x^{2}}{2} + C

Do you have a similar question?

Recalculate according to your conditions!

Didn't find what you were looking for?