Evaluate the integral by using a substitution prior to integration by parts.
-$$\int \ln \left( 10 x + 10 x ^ { 2 } \right) d x$$
A) $x \ln \left( 10 x + 10 x ^ { 2 } \right) + \ln ( x + 1 ) - 2 x + C$
B) $\ln \left( 10 x + 10 x ^ { 2 } \right) - 2 x + C$
C) $x \ln \left( 10 x + 10 x ^ { 2 } \right) + C$
D) $\ln \left( 10 x + 10 x ^ { 2 } \right) + \ln ( x + 1 ) + C$

Question

Quizplus · Accepted Answer

First, factor out the common term inside the logarithm to simplify the integral: $\int \ln(10x(1 + x))dx$. Then, use substitution $u = 10x + 10x^2$ and integration by parts to find the integral, leading to the expression $x \ln(10x + 10x^2) - \int 1 dx$, which simplifies to the answer in option A.

Evaluate the Integral by Using a Substitution Prior to Integration ∫ln⁡(10x+10x2)dx\int \ln \left( 10 x + 10 x ^ { 2 } \right) d x∫ln(10x+10x2)dx

Evaluate the Integral by Using a Substitution Prior to Integration $\int \ln \left( 10 x + 10 x ^ { 2 } \right) d x$