Math Problem Statement
∫ (x^2)/(sqrt(x^2 +5)) dx
Solution
To solve the integral
we can use a substitution method. Here's the step-by-step process:
Step 1: Substitution
Let’s set: Now, differentiate both sides with respect to :
Thus:
Now, rewrite the original integral in terms of :
This approach isn't simplifying easily. Let's try to apply integration by parts instead or look into trigonometric substitution
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Integration
Substitution Method
Trigonometric Substitution
Formulas
Substitution: u = x^2 + 5
du = 2x dx
Integration by parts: ∫u dv = uv - ∫v du
Theorems
Substitution Rule
Integration by Parts
Suitable Grade Level
Undergraduate Calculus