What is the integral of t/(sqrt(9+t^2)) ?

The integral of t/(sqrt(9+t^2)) is sqrt(9+t^2)+C

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integral of t/(sqrt(9+t^2))

\int \frac{t}{9 + t ^{2}} d t

9 + t^{2} + C

Solution steps

\int \frac{t}{9 + t ^{2}} d t

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 = 9 + t^{2}

= \frac{1}{2} \cdot 2 (9 + t^{2})^{\frac{1}{2}}

Simplify

\frac{1}{2} \cdot 2 (9 + t^{2})^{\frac{1}{2}} : 9 + t^{2}

= 9 + t^{2}

Add a constant to the solution

= 9 + t^{2} + C

\frac{\partial}{\partial m} (m x + b)

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

n = 1 \sum \infty \frac{3 ^{n}}{4 ^{n}}

\int_{9}^{16} x d x

\frac{d}{d x} (sin (\frac{π x}{8}))

What is the integral of t/(sqrt(9+t^2)) ?
The integral of t/(sqrt(9+t^2)) is sqrt(9+t^2)+C