What is the integral of (pi/(x^4)+e^2sqrt(x)) ?

The integral of (pi/(x^4)+e^2sqrt(x)) is -pi/(3x^3)+e^2 2/3 x^{3/2}+C

integral of (pi/(x^4)+e^2sqrt(x))

\int (\frac{π}{x ^{4}} + e^{2} x) d x

- \frac{π}{3 x ^{3}} + e^{2} \frac{2}{3} x^{\frac{3}{2}} + C

Solution steps

\int \frac{π}{x ^{4}} + e^{2} x d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int \frac{π}{x ^{4}} d x + \int e^{2} x d x

\int \frac{π}{x ^{4}} d x = - \frac{π}{3 x ^{3}}

\int e^{2} x d x = e^{2} \frac{2}{3} x^{\frac{3}{2}}

= - \frac{π}{3 x ^{3}} + e^{2} \frac{2}{3} x^{\frac{3}{2}}

Add a constant to the solution

= - \frac{π}{3 x ^{3}} + e^{2} \frac{2}{3} x^{\frac{3}{2}} + C

\int x cosh (a x) d x

\int \frac{a}{2 x} d x

\int \frac{3 x}{1 - 4 x ^{2}} d x

\int \frac{cos ( x )}{2 - sin ^{2} ( x )} d x

\int \frac{2 x ^{\frac{3}{2}}}{3 x} d x

What is the integral of (pi/(x^4)+e^2sqrt(x)) ?
The integral of (pi/(x^4)+e^2sqrt(x)) is -pi/(3x^3)+e^2 2/3 x^{3/2}+C