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Popular >

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

Solution

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

Solution

1 + x^{2} + C

Solution steps

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

Apply u-substitution

: \int \frac{1}{2 u} d u

= \int \frac{1}{2 u} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{2} \cdot \int \frac{1}{u} d u

Apply the Power Rule

: 2 u^{\frac{1}{2}}

= \frac{1}{2} \cdot 2 u^{\frac{1}{2}}

Substitute back

u = 1 + x^{2}

= \frac{1}{2} \cdot 2 (1 + x^{2})^{\frac{1}{2}}

Simplify

\frac{1}{2} \cdot 2 (1 + x^{2})^{\frac{1}{2}} : 1 + x^{2}

= 1 + x^{2}

Add a constant to the solution

= 1 + x^{2} + C

Popular Examples

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

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

tangent of x^3 tangent of

x^{3}

derivative of ln(xe^x)

\frac{d}{d x} (ln (x) e^{x})

derivative of (5x-4^2)

\frac{d}{d x} ((5 x - 4)^{2})

derivative of f(x)=ln(1/x)derivative of

f (x) = ln (\frac{1}{x})

Frequently Asked Questions (FAQ)

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