Question

$\large\underline{ \bf{Question:- }}$
$\: \: \: \: \: \: \: \: \displaystyle \int \sf{ \frac{x {}^{2} }{ \sqrt{x {}^{2} \: + \: 25 } } \: dx }$
[Solve it ]

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Answer 1

Answer:

Step-by-step explanation:

∫(x²/$\sqrt{x^2 +25}$) dx

= ∫((x² +25) -25)/$\sqrt{x^2 +25}$ dx

= ∫(($\sqrt{x^2 +25}$) - 25/$\sqrt{x^2 +25}$) dx

=∫ $\sqrt{x^2 +25}$ dx - ∫ 25/$\sqrt{x^2 +25}$ dx

= (x/2)$\sqrt{x^2 +25}$ + (25/2) logl x +$\sqrt{x^2 +25}$l  - 25 logl x+$\sqrt{x^2 +25}$l  +c

= (x/2)$\sqrt{x^2 +25}$  -(25/2) logl x +$\sqrt{x^2 +25}$l +c

Answer 2

• Refer to the attachment ✅