What is the integral of 2x^4+3sqrt(x)+1/(x^3) ?

The integral of 2x^4+3sqrt(x)+1/(x^3) is (2x^5)/5+2x^{3/2}-1/(2x^2)+C

Popular >

integral of 2x^4+3sqrt(x)+1/(x^3)

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

\frac{2 x ^{5}}{5} + 2 x^{\frac{3}{2}} - \frac{1}{2 x ^{2}} + C

Solution steps

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

\int 2 x^{4} d x = \frac{2 x ^{5}}{5}

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

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

= \frac{2 x ^{5}}{5} + 2 x^{\frac{3}{2}} - \frac{1}{2 x ^{2}}

Add a constant to the solution

= \frac{2 x ^{5}}{5} + 2 x^{\frac{3}{2}} - \frac{1}{2 x ^{2}} + C

\int I n^{4} x d x

\int \frac{4 arctan ( x )}{1 + x ^{2}} d x

\int (e^{x} + \frac{1}{4 x}) d x

\int x^{3} e^{x^{6}} d x

\int 1 + \frac{81 x}{64} d x

What is the integral of 2x^4+3sqrt(x)+1/(x^3) ?
The integral of 2x^4+3sqrt(x)+1/(x^3) is (2x^5)/5+2x^{3/2}-1/(2x^2)+C