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Popular >

integral of 1+x^2

Solution

\int 1 + x^{2} d x

Solution

x + \frac{x ^{3}}{3} + C

Solution steps

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

\int 1 d x = x

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

= x + \frac{x ^{3}}{3}

Add a constant to the solution

= x + \frac{x ^{3}}{3} + C

Popular Examples

sum from n=1 to infinity of 1/((n(n+8)))

n = 1 \sum \infty \frac{1}{( n ( n + 8 ) )}

derivative of e^{-6x^5}

\frac{d}{d x} (e^{- 6 x^{5}})

tangent of f(x)=x^2-7 tangent of

f (x) = x^{2} - 7

integral of 5/((x+1)(x^2+4))

\int \frac{5}{( x + 1 ) ( x ^{2} + 4 )} d x

integral of t^2sqrt(1+t^2)

\int t^{2} 1 + t^{2} d t

Frequently Asked Questions (FAQ)

What is the integral of 1+x^2 ?
The integral of 1+x^2 is x+(x^3)/3+C