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

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

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

Similar Questions

Find: $\int \cos^{2} x \, dx$

$\int \frac{dx}{\sin^2 x \cos^2 x} =$

$\int (1 + 2x + 3x^2 + 4x^3 + \dots) \, dx = $

Find the integral of the function $\frac{\sin ^{2} x}{1+\cos x}$.

Find the integral of the function $\frac{1-\cos x}{1+\cos x}$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module