Question

integration of x^3+3x+4/x

Answer 1

here is ur answer......

Answer 2

Soln:

$Let \ I = \int\ \frac{x^{3} \ + \ 3x \ + \ 4}{\sqrt {x}}\, dx$

$or, \ I = \int\  (\frac{ x^{3}}{\sqrt{x}} \ + \ \frac{3x}{\sqrt{x}} \ + \ \frac{4}{\sqrt{x}}} )\,dx$

$or, \ I = \int\ \frac{x^{3}}{\sqrt{x}}\,dx \ + \ \int\ \frac{3x}{\sqrt{x}}\,dx \ + \ \int\ \frac{4}{\sqrt{x}}\,dx$

$or, \ I = \int\ {x^{3 - \frac{1}{2}}}\,dx \ + \ 3\int\ x{^{1 - \frac{1}{2}}\,dx \ + \ 4\int\ {x}^{\frac{-1}{2}}\,dx$

$or, \ I = \int\ x^{\frac{5}{2}}\,dx \ + \ 3\int\ x^{\frac{1}{2}}\,dx \ + \ 4\int\ x^{\frac{-1}{2}}\,dx$

$or, \ I = \tfrac{2}{7}x^{\tfrac{7}{2}}\ + \ 2x^{\tfrac{3}{2}} \ + \ 8\sqrt{x} \ + \ c$