ज्ञात करें `int x^(13//2)sqrt(1+x^(5//2))dx`

Explanation

`1+x^(5//2)=z^2,` रखे, तो `5/2x^(3//2)dx2z dz`
अब, `I int x^5x^(3//2)sqrt(1+x^(5//2))dx=it(z^2-1)^2 4/5 z dz.`
`4/2int(z^4-2z^2+1)z^2dz=4/5int(z^6 - 2z^4+z^2)dz`
`=4/5[z^7/7-2*z^5/5+z^3/3]+c` जहां `z=sqrt(1+x^(5//2))`