1
$\begingroup$

I have been unable to solve this integral $$f(x)= \int e^x \left(\frac{x^4+2}{(1+x^2)^{5/2}}\right)dx$$

I tried to solve the expression by trying to make the expression come into the form of $$e^x(g(x)+g'(x))dx$$ but I have been unable to carry out any manipulation to make the expression come into this form. Kindly help me in solving this integration.

P.S. One of the tricks that my book used was to divide the expressions and then solving the integral. Kindly suggest some other method which deals completely with algebraic manipulation.

  • 1
    $$\dfrac{d\left(\dfrac{e^x(A+Bx+Cx^2)}{(1+x^2)^{3/2}}\right)}{dx}=?$$ – 2017-01-25

1 Answers 1

0

we have $$g(x)+g'(x)=\frac{x^4+2}{(1+x^2)^{5/2}}$$ solving this equation we get $$g(x)=\frac{x^2+x+1}{(x^2+1)^{3/2}}$$

  • 1
    IMHO, it'll be better to include the steps for solving this equation. – 2017-01-25
  • 0
    Perhaps your $g$ should be $(1+x+x^2)/(1+x^2)^{3/2}$? – 2017-01-25