Apa itu int xln (x) ^ 2?

Apa itu int xln (x) ^ 2?
Anonim

Menjawab:

Misalkan Anda maksud #ln (x) ^ 2 = (lnx) ^ 2 #

Anda harus berintegrasi dengan bagian dua kali. Jawabannya adalah:

# x ^ 2/2 (ln (x) ^ 2-lnx + 1/2) + c #

Misalkan Anda maksud # ln (x) ^ 2 = ln (x ^ 2) #

Anda harus berintegrasi dengan bagian sekali. Jawabannya adalah:

# x ^ 2 (lnx-1/2) + c #

Penjelasan:

Misalkan Anda maksud #ln (x) ^ 2 = (lnx) ^ 2 #

#intxln (x) ^ 2dx = #

# = int (x ^ 2/2) 'ln (x) ^ 2dx = #

# = x ^ 2 / 2ln (x) ^ 2-intx ^ 2/2 (ln (x) ^ 2) 'dx = #

# = x ^ 2 / 2ln (x) ^ 2-intx ^ membatalkan (2) / membatalkan (2) * membatalkan (2) lnx * 1 / membatalkan (x) dx = #

# = x ^ 2 / 2ln (x) ^ 2-intxlnxdx = #

# = x ^ 2 / 2ln (x) ^ 2-int (x ^ 2/2) 'lnxdx = #

# = x ^ 2 / 2ln (x) ^ 2- (x ^ 2 / 2lnx-intx ^ 2/2 (lnx) 'dx) = #

# = x ^ 2 / 2ln (x) ^ 2- (x ^ 2 / 2lnx-intx ^ batal (2) / 2 * 1 / batal (x) dx) = #

# = x ^ 2 / 2ln (x) ^ 2- (x ^ 2 / 2lnx-1 / 2intxdx) = #

# = x ^ 2 / 2ln (x) ^ 2- (x ^ 2 / 2lnx-1 / 2x ^ 2/2) + c = #

# = x ^ 2 / 2ln (x) ^ 2- (x ^ 2 / 2lnx-x ^ 2/4) + c = #

# = x ^ 2 / 2ln (x) ^ 2-x ^ 2 / 2lnx + x ^ 2/4 + c = #

# = x ^ 2/2 (ln (x) ^ 2-lnx + 1/2) + c #

Misalkan Anda maksud # ln (x) ^ 2 = ln (x ^ 2) #

#intxln (x) ^ 2dx = intx * 2lnxdx #

# 2intxlnxdx = #

# = 2int (x ^ 2/2) 'lnxdx = #

# = 2 (x ^ 2 / 2lnx-intx ^ 2/2 * (lnx) 'dx) = #

# = 2 (x ^ 2 / 2lnx-intx ^ batal (2) / 2 * 1 / batal (x) dx) = #

# = 2 (x ^ 2 / 2lnx-1 / 2intxdx) = #

# = 2 (x ^ 2 / 2lnx-1 / 2x ^ 2/2) + c = #

# = batal (2) * x ^ 2 / (batal (2)) (lnx-1/2) + c = #

# = x ^ 2 (lnx-1/2) + c #