Find the given indefinite integral.
-$\int \ln (7 x+8) d x$
A) $\left.\frac{1}{7} 56 x-\ln (7 x+8)-(7 x+8)\right]+C$
B) $\frac{1}{7}[(7 x+8) \ln x-(7 x+8)]+C$
C) $\frac{1}{7}[(7 x+8) \ln (7 x+8)-(7 x+8)]+C$
D) $\frac{1}{7}[(7 x+8) \ln (7 x+8)-(7 x+8)-56]+C$

Question

Quizplus · Accepted Answer

Integration by parts with $u=\ln (7x+8)$ and $dv=dx$ gives $du=\frac{7}{7x+8}dx$ and $v=x$. So,$\int \ln (7 x+8) d x=x \ln (7 x+8)-\int x \frac{7}{7x+8}dx$$\int \ln (7 x+8) d x=x \ln (7 x+8)-\int \frac{7x}{7x+8}dx$$\int \ln (7 x+8) d x=x \ln (7 x+8)-\frac{7}{7}\ln (7x+8)+C$$\int \ln (7 x+8) d x=\frac{1}{7}[(7 x+8) \ln (7 x+8)-(7 x+8)]+C$

Find the Given Indefinite Integral ∫ln⁡(7x+8)dx\int \ln (7 x+8) d x∫ln(7x+8)dx

Find the Given Indefinite Integral $\int \ln (7 x+8) d x$