Question

Q1. The value of ſ Inx dx is O(A) xlnx + xto O (B) xlnx + c O (C) xlnx - x +o O (D) xlnx - x​

Answer 1

Step-by-step explanation:

∫

x

e

x

(1+xlnx)dx

=∫

x

e

x

dx+∫

x

e

x

xlnxdx

=∫

x

e

x

dx+∫e

x

lnxdx

Consider ∫

x

e

x

dx

Integrating by parts,

Let u=e

x

⇒du=e

x

dx

dv=

x

1

dx⇒v=lnx

=e

x

lnx−∫lnxe

x

dx

∴∫

x

e

x

dx=e

x

lnx−∫lnxe

x

dx+c

∴∫

x

e

x

dx+∫e

x

lnxdx

=e

x

lnx−∫lnxe

x

dx+∫lnxe

x

dx+c

=e

x

lnx+c where c is the constant of integration.