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Popular >

integral of 1/(x^2)+1

Solution

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

Solution

- \frac{1}{x} + x + C

Solution steps

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

Apply exponent rule:

\frac{1}{a ^{b}} = a^{- b}

\frac{1}{x ^{2}} = x^{- 2}

= \int x^{- 2} + 1 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 x^{- 2} d x + \int 1 d x

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

\int 1 d x = x

= - \frac{1}{x} + x

Add a constant to the solution

= - \frac{1}{x} + x + C

Graph

Popular Examples

sum from n=2 to infinity of 3/(5^n)

n = 2 \sum \infty \frac{3}{5 ^{n}}

derivative of-x^4-4/3 x^3+4x^2

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

integral of (sin(x)+2cos(x))

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

derivative of x^t

\frac{d}{d x} (x^{t})

integral from 0 to 4 of (2t+4)^{-1/2}

\int_{0}^{4} (2 t + 4)^{- \frac{1}{2}} d t

Frequently Asked Questions (FAQ)

What is the integral of 1/(x^2)+1 ?
The integral of 1/(x^2)+1 is -1/x+x+C