What is the integral of 1/(t^2sqrt(400-t^2)) ?

The integral of 1/(t^2sqrt(400-t^2)) is -(sqrt(400-t^2))/(400t)+C

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integral of 1/(t^2sqrt(400-t^2))

\int \frac{1}{t ^{2} 400 - t ^{2}} d t

- \frac{400 - t ^{2}}{400 t} + C

Solution steps

\int \frac{1}{t ^{2} 400 - t ^{2}} d t

Apply Trigonometric Substitution

: \int \frac{cot ( u )}{400 cos ( u ) sin ( u )} d u

= \int \frac{cot ( u )}{400 cos ( u ) sin ( u )} d u

Take the constant out:

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

= \frac{1}{400} \cdot \int \frac{cot ( u )}{cos ( u ) sin ( u )} d u

Simplify

\frac{cot ( u )}{cos ( u ) sin ( u )} : csc^{2} (u)

= \frac{1}{400} \cdot \int csc^{2} (u) d u

Use the common integral:

\int csc^{2} (u) d u = - cot (u)

= \frac{1}{400} (- cot (u))

Substitute back

u = arcsin (\frac{1}{20} t)

= \frac{1}{400} (- cot (arcsin (\frac{1}{20} t)))

Simplify

\frac{1}{400} (- cot (arcsin (\frac{1}{20} t))) : - \frac{400 - t ^{2}}{400 t}

= - \frac{400 - t ^{2}}{400 t}

Add a constant to the solution

= - \frac{400 - t ^{2}}{400 t} + C

\frac{d}{d x} (cos (arctan (3 x)))

\int_{0}^{\frac{1}{10}} x ln (10 x) d x

x \to 0 lim (2)

f (x) = 3 tan (x), at x = \frac{π}{3}

\int_{- \infty}^{0} x d x

What is the integral of 1/(t^2sqrt(400-t^2)) ?
The integral of 1/(t^2sqrt(400-t^2)) is -(sqrt(400-t^2))/(400t)+C