# How do you integrate #int xsqrt(2x^2+7)# using substitution?

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To integrate ( \int x\sqrt{2x^2+7} ) using substitution, we can use the substitution method ( u = 2x^2 + 7 ). This leads to ( du = 4x , dx ). After finding ( du ), we can then rewrite the integral in terms of ( u ). This yields ( \frac{1}{4} \int \sqrt{u} , du ). Integrating ( \sqrt{u} ) yields ( \frac{2}{3}u^{3/2} + C ). Finally, substituting back ( u = 2x^2 + 7 ) gives the final answer ( \frac{2}{3}(2x^2 + 7)^{3/2} + C ).

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To integrate ∫x√(2x^2 + 7) using substitution, let u = 2x^2 + 7.

Then, differentiate u with respect to x to find du/dx.

Next, solve for dx in terms of du using the differentiation.

Substitute u and dx into the integral.

Now, integrate the expression with respect to u.

Finally, substitute back for x in terms of u to get the final result.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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