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evaluate ∫ {x^3 – 3(x)^2 + 5x – 7 +x^2 a^x} / 2(x)^2 dx

evaluate
∫  {x^3 – 3(x)^2 + 5x – 7 +x^2 a^x} / 2(x)^2 dx

Grade:12

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
6 years ago
Ans:
Hello Student,
Please find answer to your question below

I = \int \frac{x^3-3x^2+5x-7+x^2a^{x}}{2x^2}dx
I = \frac{1}{2}\int \frac{x^3-3x^2+5x-7+x^2a^{x}}{x^2}dx
I = \frac{1}{2}\int (x-3+\frac{5}{x}-\frac{7}{x^2}+a^{x})dx
I = \frac{1}{2}[\int xdx-\int 3dx+\int \frac{5}{x}dx-\int \frac{7}{x^2}dx+\int a^{x}dx]
I = \frac{1}{2}[\frac{x^2}{2}-\int 3dx+\int \frac{5}{x}dx-\int \frac{7}{x^2}dx+\int a^{x}dx]
I = \frac{1}{2}[\frac{x^2}{2}-3x+\int \frac{5}{x}dx-\int \frac{7}{x^2}dx+\int a^{x}dx]
I = \frac{1}{2}[\frac{x^2}{2}-3x+5lnx-\int \frac{7}{x^2}dx+\int a^{x}dx]
I = \frac{1}{2}[\frac{x^2}{2}-3x+5lnx+ \frac{7}{x}+\int a^{x}dx]
I = \frac{1}{2}[\frac{x^2}{2}-3x+5lnx+ \frac{7}{x}+\frac{a^{x}}{ln2}]+c

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