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Evaluate: (i) intxcos^3x^2sinx^2\ dx (ii...

Evaluate: (i) `intxcos^3x^2sinx^2\ dx` (ii) `intsin^7x\ dx`

Text Solution

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(i) `int x cdot cos ^{3} x^{2} sin x^{2} d x `
`text { Let } x^{2}=t `
`Rightarrow 2 x d x=d t `
`Rightarrow x dx=frac{d t}{2} `
`text { Now, } int x cdot cos ^{3} x^{2} sin x^{2} d x `
`=frac{1}{2} int cos ^{3} t cdot sin t . d t `
...
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