Question

$\int{{{x}^{2}}\,{{7}^{x}}\,\,dx}$ is equal to

• A. $\frac{{{x}^{2}}{{7}^{x}}}{\log \,7}+2x\frac{{{7}^{x}}}{{{(\log \,7)}^{2}}}+2\frac{{{7}^{x}}}{{{(\log \,7)}^{3}}}+c$
• B. $\frac{{{x}^{2}}{{7}^{x}}}{\log \,7}-2x\frac{{{7}^{x}}}{{{(\log \,7)}^{2}}}+2\frac{{{7}^{x}}}{{{(\log \,7)}^{3}}}+c$
• C. ${{x}^{2}}{{7}^{x}}-2x\,\frac{7x}{\log \,7}+2\,\frac{7x}{{{(\log \,7)}^{2}}}+c$
• D. $\frac{{{x}^{2}}{{7}^{x}}}{{{(\log \,7)}^{2}}}-2x\,\frac{{{7}^{x}}}{{{(\log \,7)}^{3}}}+2\frac{{{7}^{x}}}{{{(\log \,7)}^{4}}}+c$

Answer 1

Answer: (B)

$\frac{{{x}^{2}}{{7}^{x}}}{\log \,7}-2x\frac{{{7}^{x}}}{{{(\log \,7)}^{2}}}+2\frac{{{7}^{x}}}{{{(\log \,7)}^{3}}}+c$

Answer 2

$\int{{{x}^{2}}}\,.\,\,{{7}^{x}}\,\,dx$
$=\frac{{{x}^{2}}{{.7}^{x}}}{\log \,7}-\int{\frac{2x.\,{{7}^{x}}}{log\,7}}\,dx+c$
$=\frac{{{x}^{2}}{{.7}^{x}}}{\log 7}-\frac{2}{\log 7}[\int{x{{.7}^{x}}\,dx]+c}$