Find-the-Integration-Value-1-x-d-x-1-3-x-2-dx-x-1-2-x-1-4-

Question Number 140330 by Satyendra last updated on 06/May/21

F i n d t h e I n t e g r a t i o n V a l u e :

1 \int \frac{\sqrt{x} d (x)}{1 +^{3} \sqrt{x}} = ?

2 \int \frac{d x}{x^{\frac{1}{2}} - x^{\frac{1}{4}}} = ?

Answered by john_santu last updated on 06/May/21

(1) l e t x = t^{6} \to d x = 6 t^{5} d t

I = \int \frac{t^{3}}{1 + t^{2}} (6 t^{5} d t)

I = \int \frac{6 t^{8}}{1 + t^{2}} d t .

n o w i t e a s y t o s o l v e

Answered by benjo_mathlover last updated on 06/May/21

(2) I = \int \frac{dx}{\sqrt{x} - \sqrt[4]{x}}

let x = z^{4} \to dx = {4 z}^{3} dz

I = \int \frac{{4 z}^{3}}{z^{2} - z} dz = \int \frac{{4 z}^{2}}{z - 1} dz

use partial fraction