How to integrate: \(\displaystyle{\int_{{\sqrt{{{\ln{{2}}}}}}}^{{\sqrt{{{\ln{{3}}}}}}}}{\frac{{{x}\cdot{\sin{{\left({x}^{{2}}\right)}}}}}{{{\sin{{\left({x}^{{2}}\right)}}}+{\sin{{\left({\ln{{6}}}-{x}^{{2}}\right)}}}}}}{\left.{d}{x}\right.}\)

Jasiah Vincent

Jasiah Vincent

Answered question

2022-04-06

How to integrate:
ln2ln3xsin(x2)sin(x2)+sin(ln6x2)dx

Answer & Explanation

resacarno4u

resacarno4u

Beginner2022-04-07Added 12 answers

Substituting x2=t After doing this your integral becomes
I=12ln2ln3sintsint+sin(ln6-t)dt
Next, use this formula:
abf(x)  dx =abf(a+bx)  dx 
Also you have
I=12ln2ln3sin(ln6-t)sint+sin(ln6-t) dt    (2)

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