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Popular >

integral of 3/x+x^3

Solution

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

Solution

3 ln ∣ x ∣ + \frac{x ^{4}}{4} + C

Solution steps

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

\int \frac{3}{x} d x = 3 ln ∣ x ∣

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

= 3 ln ∣ x ∣ + \frac{x ^{4}}{4}

Add a constant to the solution

= 3 ln ∣ x ∣ + \frac{x ^{4}}{4} + C

Popular Examples

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(dx)/(dt)=sin(3t)cos(3t)

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derivative of x^3-17x^2+63x+6 derivative of

x^{3} - 17 x^{2} + 63 x + 6

(\partial)/(\partial x)(x^2+y^2+3z)

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integral of (2x)cos(x)

\int (2 x) cos (x) d x

Frequently Asked Questions (FAQ)

What is the integral of 3/x+x^3 ?
The integral of 3/x+x^3 is 3ln|x|+(x^4)/4+C