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Evaluate: (i) int4\ x^3\ sqrt(5-x^2)\ dx...

Evaluate: (i) `int4\ x^3\ sqrt(5-x^2)\ dx` (ii) `int1/(sqrt(x)+x)\ dx`

Text Solution

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(i) `int 4 x^{3} sqrt{5-x^{2}} d x `
`=4 int x^{2} times x sqrt{5-x^{2}} dx `
`text { Let } 5-x^{2}=t `
`Rightarrow x^{2}=5-t `
`Rightarrow 2 x=-frac{d t}{d x} `
`Rightarrow x dx=-frac{d t}{2} `
...
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