Evaluate the following indefinite integral. int ( {frac{e}{x^4} + 2 sqrt{x}} )dx (Use C as...

Question:

Evaluate the following indefinite integral.

{eq}\int \left ( {\frac{e}{x^4} + 2 \sqrt{x}} \right )dx {/eq}

(Use {eq}C {/eq} as the arbitrary constant)

Indefinite Integral:

When the indefinite integral is evaluated or when we start solving the integral, we first check the expression in the integrand and apply the rule of integration accordingly. Like we have used the power rule: {eq}\int x^adx=\frac{x^{a+1}}{a+1}+c {/eq}

We have to integrate:

{eq}\int \left( {\frac{e}{x^4} + 2 \sqrt{x}} \right)dx\\ {/eq}

Now, this is done by applying the power rule of integration, that is given as follows:

Hence we have the integral as:

{eq}\int \frac{e}{x^4}+2\sqrt{x}dx\\ =\int \frac{e}{x^4}dx+\int \:2\sqrt{x}dx\\ =-\frac{e}{3x^3}+\frac{4}{3}x^{\frac{3}{2}}+C {/eq}