integration 2

[ivory blade]

i tried opening the underroot term and then completing the square. doesnt work

[subtle prawn]

<@&1227988399579730072>

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[elfin gull]

whats the answer

cant we just use integral sqrt(a^2-x^2)

[ivory blade]

whi try kia tha

thoda thoda same aaya but somehow arcsin(root(x-1)) hai ans mein

[manic timber]

Idts the ans should be this im getting t/4-sin(4t)/16 where t is arcsin(root(x-1))

Checked on wolfram

[ivory blade]

kholkar yeh bana /

ans key says this

arcsin() ke alawa sab shi aa rha

[manic timber]

Yea u cn do like this

[ivory blade]

what about directly applying that IBP formula here

[manic timber]

whats the ibp formula

[manic timber]

these 2 terms are equivalent u can prove it using a substituion they differ by pi/2

[ivory blade]

bruh how am i supposed to know this in exam 😭