In each part, use the substitution to replace the given integralwith an integral

Chapter 5, Problem 2

(choose chapter or problem)

In each part, use the substitution to replace the given integral with an integral involving the variable $u$. (Do not evaluate the integral.)

(a) $\int_{0}^{2} 3 x^{2}\left(1+x^{3}\right)^{3} d x, u=1+x^{3}$

(b) $\int_{0}^{2} \frac{x}{\sqrt{5-x}} d x ; u=5-x^{2}$

Equation Transcription:

$u$

$\int\limits_{0}^{2}\ {3{x}^{2}\ (1\ +\ {x}^{3}{)}^{3}\ dx;\ u\ =\ 1\ +\ {x}^{3}}^{\ }$

$\int\limits_{0}^{2}\ \frac{x}{{\sqrt{5\ -\ x}}^{2}}\ dx;\ u\ =\ 5\ -\ {x}^{2}$

$\int\limits_{0}^{1}\ \frac{{e}^{\sqrt{x}}}{\sqrt{x}\ }\ dx;\ u\ =\ \sqrt{x}$

Text Transcription:

int_{0}^{2} 3 x^2(1+x^{3})^{3} dx, u = 1 + x^3

int_{0}^{2} frac{x}{sqrt{5-x}} dx ; u = 5 - x^2

int_{0}^{1} frac{e^{sqrt x}{sqrt x} dx ; u = sqrt x

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