Doy un total de 30 puntos por estas dos preguntas la deje el la imagen quien me pueda ayudar muchas gracias?

1. - <img src="https://tex.z-dn.net/?f=%20%5Cint%5Climits%5E1_0%20%7B%285x%2B4%29%7D%20%5C%2C%20dx%20%5C%5C%3D5%5Cfrac%7Bx%5E2%7D%7B2%7D%2B4x%20%5Cbigg%5Crvert%5E1_0%3D%5Cfrac%7B5%7D%7B2%7D%2B4%3D%5Cfrac%7B13%7D%7B2%7D%20" /> 2. - <img src="https://tex.z-dn.net/?f=%20%5Cint%20%7B5%5Exx%5E2%7D%20%5C%2C%20dx%20" /> Se procede a integrar por partes : <img src="https://tex.z-dn.net/?f=%20%5Cint%20%7Bu%7D%20%5C%2C%20dv%3Duv-%5Cint%20%7Bv%7D%20%5C%2C%20du%5C%5C%20%5C%5Ccon%3A%5C%5Cu%3Dx%5E2%5Cqquad%20du%3D2x%5C%2Cdx%5C%5Cdv%3D5%5Ex%5C%2Cdx%5Cqquad%20v%3D%5Cfrac%7B5%5Ex%7D%7Bln%5C%2Cx%7D%20" /> <img src="https://tex.z-dn.net/?f=%20%5Cint%20%7B5%5Exx%5E2%7D%20%5C%2C%20dx%3D%5Cfrac%7Bx%5E25%5Ex%7D%7Bln%5C%2C5%7D-%5Cfrac%7B2%7D%7Bln%5C%2C5%7D%5Cint%20%7Bx5%5Ex%7D%20%5C%2C%20dx%20" /> esta ultima integral se integra de nuevo por partes con : <img src="https://tex.z-dn.net/?f=%20u%3Dx%5Cqquad%20du%3Ddx%5C%5Cdv%3D5%5Ex%5C%2Cdx%5Cqquad%20v%3D%5Cfrac%7B5%5Ex%7D%7Bln%5C%2Cx%7D%20" /> Entonces : <img src="https://tex.z-dn.net/?f=%20%5Cint%20%7B5%5Exx%5E2%7D%20%5C%2C%20dx%3D%5Cfrac%7Bx%5E25%5Ex%7D%7Bln%5C%2C5%7D-%5Cfrac%7B2%7D%7Bln%5C%2C5%7D%28%5Cfrac%7Bx5%5Ex%7D%7Bln%5C%2C5%7D-%5Cfrac%7B1%7D%7Bln%20%5C%2C5%7D%5Cint%20%7B5%5Ex%7D%20%5C%2Cdx%29%5C%5C%20%5C%5C%3D%5Cfrac%7Bx%5E25%5Ex%7D%7Bln%5C%2C5%7D-%5Cfrac%7B2%7D%7Bln%5C%2C5%7D%28%5Cfrac%7Bx5%5Ex%7D%7Bln%5C%2C5%7D-%5Cfrac%7B1%7D%7Bln%20%5C%2C5%7D%5Cfrac%7B5%5Ex%7D%7Bln%5C%2C5%7D%29%5C%5C%20%5C%5C%3D%5Cfrac%7Bx%5E25%5Ex%7D%7Bln%5C%2C5%7D-%5Cfrac%7B2x5%5Ex%7D%7B%28ln%5C%2C5%29%5E2%7D%2B%5Cfrac%7B2%285%5Ex%29%7D%7B%28ln%5C%2C5%29%5E3%7D%5C%5C%20%5C%5C%3D%5Cfrac%7B5%5Ex%7D%7Bln%5C%2C5%7D%5Bx%5E2-%5Cfrac%7B2x%7D%7Bln%5C%2C5%7D%2B%5Cfrac%7B2%7D%7B%28ln%5C%2C5%29%5E2%7D%5D%20" />.