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Evaluate the Integral $\int 15 x \ln (1+x) d x$ A) $15\left(\frac{1}{6} x^{2}-\frac{1}{9} x^{3}+\frac{x^{3}}{3} \ln (1+x)+\frac{1}{3} \ln (1+x)\right)+C$

Question 9

Multiple Choice

Evaluate the integral. $\int 15 x \ln (1+x) d x$

A) $15\left(\frac{1}{6} x^{2}-\frac{1}{9} x^{3}+\frac{x^{3}}{3} \ln (1+x) +\frac{1}{3} \ln (1+x) \right) +C$
B) $\frac{15}{4}\left(2\left(x^{2}-1\right) \ln (1+x) -x(x-2) \right) +C$
C) $15\left(\frac{1}{4} x^{2}-\frac{1}{2} \ln (1+x) +\frac{x^{2}}{2}(\ln (1+x) ) \right) +C$
D) $\frac{15}{4}\left(2\left(x^{2}-1\right) \ln (1+x) +x(x-2) \right) +C$
E) $15\left(-\frac{1}{3} x+\frac{1}{6} x^{2}-\frac{1}{9} x^{4}+\frac{1}{3} \ln (1+x) \right) +C$

Evaluate the Integral ∫15xln⁡(1+x)dx\int 15 x \ln (1+x) d x∫15xln(1+x)dx A) 15(16x2−19x3+x33ln⁡(1+x)+13ln⁡(1+x))+C15\left(\frac{1}{6} x^{2}-\frac{1}{9} x^{3}+\frac{x^{3}}{3} \ln (1+x)+\frac{1}{3} \ln (1+x)\right)+C15(61​x2−91​x3+3x3​ln(1+x)+31​ln(1+x))+C

Multiple Choice

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Evaluate the Integral $\int 15 x \ln (1+x) d x$ A) $15\left(\frac{1}{6} x^{2}-\frac{1}{9} x^{3}+\frac{x^{3}}{3} \ln (1+x)+\frac{1}{3} \ln (1+x)\right)+C$

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