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Popular >

integral of x/(sqrt(27+x^2))

Solution

\int \frac{x}{27 + x ^{2}} d x

Solution

27 + x^{2} + C

Solution steps

\int \frac{x}{27 + 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 = 27 + x^{2}

= \frac{1}{2} \cdot 2 (27 + x^{2})^{\frac{1}{2}}

Simplify

\frac{1}{2} \cdot 2 (27 + x^{2})^{\frac{1}{2}} : 27 + x^{2}

= 27 + x^{2}

Add a constant to the solution

= 27 + x^{2} + C

Graph

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Frequently Asked Questions (FAQ)

What is the integral of x/(sqrt(27+x^2)) ?
The integral of x/(sqrt(27+x^2)) is sqrt(27+x^2)+C