Vault Of Euclid

Integral of x times the square root of 1+x

Techniques of integration core

Find \( \int x\sqrt{1+x} \, dx \).

The solution and a full step-by-step explanation are here. Sign in to read them.

What you need first

Integration by parts
Power rule for integration
Factoring algebraic expressions with fractional exponents

What this problem tests

Tests the application of integration by parts and algebraic manipulation of fractional exponents.

This is a standard integration problem found in Calculus I or II courses, testing the ability to apply integration by parts and simplify the result.

More on Techniques of integration

Integral of ln(x) / x^2 warmup
Integral of a Rational Function using Partial Fractions core
Reduction Formula for x^n sin(ax) core
Integral of x^2 arctan(x) core
Reduction Formula for a Rational Function core
Area Under the Curve of ln(x)/x warmup

← today's set