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Popular >

integral of-3x^2+1/x

Solution

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

Solution

- x^{3} + ln ∣ x ∣ + C

Solution steps

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

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

\int \frac{1}{x} d x = ln ∣ x ∣

= - x^{3} + ln ∣ x ∣

Add a constant to the solution

= - x^{3} + ln ∣ x ∣ + C

Popular Examples

integral of 5/(x(ln(x))^3)

\int \frac{5}{x ( ln ( x ) ) ^{3}} d x

integral of (sec^2(x))/(sqrt(25-tan^2(x)))

\int \frac{sec ^{2} ( x )}{25 - tan ^{2} ( x )} d x

integral of (x^2)/(1+x^2)arctan(x)

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

integral of 1/(sin^2(x)+2cos^2(x))

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

integral of (6-6x)/(6x-3x^2)

\int \frac{6 - 6 x}{6 x - 3 x ^{2}} d x

Frequently Asked Questions (FAQ)

What is the integral of-3x^2+1/x ?
The integral of-3x^2+1/x is -x^3+ln|x|+C