Evaluate the following integrals:

Question:

Evaluate the following integrals:

$\int\left(2^{x}+\frac{5}{x}-\frac{1}{x^{1 / 3}}\right) d x$

Solution:

$\int\left(2^{x}+\frac{5}{x}-\frac{1}{x^{1 / 3}}\right) d x$

By Splitting them, we get,

$\Rightarrow \int 2^{\mathrm{x}} \mathrm{dx}+\int\left(\frac{5}{\mathrm{x}}\right) \mathrm{dx}-\int \frac{1}{\mathrm{x}^{1 / 3}} \mathrm{dx}$

By using the formula,

$\int a^{x} d x=\frac{a^{x}}{\log a}$

$\Rightarrow \frac{2^{x}}{\log 2}+5 \int\left(\frac{1}{x}\right) d x-\int x^{-1 / 3} d x$

By using the formula,

$\int\left(\frac{1}{x}\right) d x=\log x$

$\Rightarrow \frac{2^{x}}{\log 2}+5 \log x-\int x^{-1 / 3} d x$

By using the formula,

$\int x^{n} d x=\frac{x^{n+1}}{n+1}$

$\Rightarrow \frac{2^{x}}{\log 2}+5 \log x-\frac{x^{\frac{1}{3}+1}}{-\frac{1}{3}+1}$

$\Rightarrow \frac{2^{x}}{\log 2}+5 \log x-\frac{x^{\frac{2}{3}}}{2 / 3}$

$\Rightarrow \frac{2^{x}}{\log 2}+5 \log x-\frac{3}{2} x^{2 / 3}+c$

Leave a comment

None
Free Study Material