int left{ frac{x}{a} + frac{b}{x} + x^a + b^x | vedclass

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Question

(B) We need to evaluate the integral: $\int \left( \frac{x}{a} + \frac{b}{x} + x^a + b^x + ab \right) dx$ Applying the linearity property of integrati

Vedclass · Accepted Answer

$\frac{x^2}{2a} + b \log |x| + \frac{x^{a+1}}{a+1} + \frac{b^x}{\log b} + abx + C$

Vedclass · Answer

(B) We need to evaluate the integral: $\int \left( \frac{x}{a} + \frac{b}{x} + x^a + b^x + ab \right) dx$ Applying the linearity property of integration: $= \int \frac{x}{a} dx + \int \frac{b}{x} dx + \int x^a dx + \int b^x dx + \int ab dx$ $= \frac{1}{a} \int x dx + b \int \frac{1}{x} dx + \int x^a dx + \int b^x dx + ab \int 1 dx$ Using standard integration formulas: $= \frac{1}{a} \cdot \frac{x^2}{2} + b \log |x| + \frac{x^{a+1}}{a+1} + \frac{b^x}{\log b} + abx + C$ $= \frac{x^2}{2a} + b \log |x| + \frac{x^{a+1}}{a+1} + \frac{b^x}{\log b} + abx + C$

$\int \left\{ \frac{x}{a} + \frac{b}{x} + x^a + b^x + ab \right\} dx$ is equal to

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