# Evaluate the Integrals

A. Evaluate âˆ« x(sqrt(x+1))dx

B. Find the area bounded by y= x/(1+x)^2, y=0, x=0, and x=2

C. Evaluate âˆ« 1/x(sqrt(x+9))dx

D. Find the indefinite integral using integration by parts: âˆ«x^2(e^2x)dx

Infinity

Evaluate the improper integral: âˆ« ln(x)dx

0

F.

Evaluate âˆ«x(e^3x)dx

keywords: integrates, integration, integrated

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A.

To solve the integral we use a substitution:

Since we obtain:

B.

The area ...

#### Solution Summary

Integrals are found. The solution is detailed and well presented. The expert evaluates the improper integral functions.