What is the integral of (3x^5-6sqrt(x)+e^x-4/x) ?

The integral of (3x^5-6sqrt(x)+e^x-4/x) is (x^6)/2-4x^{3/2}+e^x-4ln|x|+C

Popular >

integral of (3x^5-6sqrt(x)+e^x-4/x)

\int (3 x^{5} - 6 x + e^{x} - \frac{4}{x}) d x

\frac{x ^{6}}{2} - 4 x^{\frac{3}{2}} + e^{x} - 4 ln ∣ x ∣ + C

Solution steps

\int 3 x^{5} - 6 x + e^{x} - \frac{4}{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 3 x^{5} d x - \int 6 x d x + \int e^{x} d x - \int \frac{4}{x} d x

\int 3 x^{5} d x = \frac{x ^{6}}{2}

\int 6 x d x = 4 x^{\frac{3}{2}}

\int e^{x} d x = e^{x}

\int \frac{4}{x} d x = 4 ln ∣ x ∣

= \frac{x ^{6}}{2} - 4 x^{\frac{3}{2}} + e^{x} - 4 ln ∣ x ∣

Add a constant to the solution

= \frac{x ^{6}}{2} - 4 x^{\frac{3}{2}} + e^{x} - 4 ln ∣ x ∣ + C

\frac{\partial}{\partial x} (x cos (y) - y cos (x))

g (x) = ln (x e^{- 2 x})

\int \frac{x ^{4} + 10 x ^{3}}{2 x ^{2}} d x

\int 2 (1 - 3 x)^{2} d x

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

What is the integral of (3x^5-6sqrt(x)+e^x-4/x) ?
The integral of (3x^5-6sqrt(x)+e^x-4/x) is (x^6)/2-4x^{3/2}+e^x-4ln|x|+C