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

The integral of (4x^3-3sqrt(x)+2/(3x^4)) is x^4-2x^{3/2}-2/(9x^3)+C

Popular >

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

\int (4 x^{3} - 3 x + \frac{2}{3 x ^{4}}) d x

x^{4} - 2 x^{\frac{3}{2}} - \frac{2}{9 x ^{3}} + C

Solution steps

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

\int 4 x^{3} d x = x^{4}

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

\int \frac{2}{3 x ^{4}} d x = - \frac{2}{9 x ^{3}}

= x^{4} - 2 x^{\frac{3}{2}} - \frac{2}{9 x ^{3}}

Add a constant to the solution

= x^{4} - 2 x^{\frac{3}{2}} - \frac{2}{9 x ^{3}} + C

\int (\frac{x - x}{3}) d x

\int \frac{7 x - 1}{x ^{2} + x - 2} d x

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

\int 30 csc (5 x) sec (5 x) d x

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

What is the integral of (4x^3-3sqrt(x)+2/(3x^4)) ?
The integral of (4x^3-3sqrt(x)+2/(3x^4)) is x^4-2x^{3/2}-2/(9x^3)+C