Calculus 2

Evaluate $\displaystyle \int \frac{\sqrt{2x^2 - 1}}{x} \, dx$ using trigonometric substitution.

Evaluate $\displaystyle \int \frac{1}{(x^2 + 1)^2} \, dx$ using an appropriate substitution method.

Evaluate $\displaystyle \int \frac{\sqrt{4 - x^2}}{x^2} \, dx$ from $\sqrt{2}$ to 2 using trigonometric substitution.

Using trigonometric substitution, integrate the following expressions: $\sqrt{a^2 - x^2}$, $\sqrt{a^2 + x^2}$, and $\sqrt{x^2 - a^2}$.

Integrate $\frac{y^2}{(16-y^2)^{3/2}}$ with respect to $y$.

Integrate $\frac{\sqrt{x^2 + 36}}{9x^2}$ with respect to $x$.

Evaluate the definite integral $\displaystyle \int_{9}^{18/\sqrt{3}} \frac{dt}{t\sqrt{t^2 - 81}}$ using trigonometric substitution.

Solve $\displaystyle \int \sin^3 x \cos^4 x \, dx$ using the substitution method where the power of sine is odd.

Solve $\displaystyle \int \sin^4 x \, dx$ using trigonometric identities for even powers.

Solve $\displaystyle \int \sin^2 x \cos^2 x \, dx$ using double angle or half angle formulas for the even powers.

Find the area under the curve $y = \sqrt{1 - x^2}$ from $x = 0$ to $x = 1$ using trigonometric substitution.

Evaluate $\displaystyle \int_{0}^{\frac{1}{2}} \sqrt{1-x^2} \, dx$ using trigonometric substitution, where $x=\sin\theta$.

Perform a trigonometric substitution for evaluating the integral involving inverse substitution where $x=\frac{1}{2}u$.

Evaluate the integral using trigonometric substitution where $x = 3 \sin \theta$ for the expression involving $\sqrt{9 - x^2}$.

Use trigonometric substitution to solve the integral involving a square root: integrate from $-3$ to $3$ the square root of $9 - x^2$ $dx$.

Using trigonometric substitution, solve integrals that have integrals involving $a^2 - u^2$, $a^2 + u^2$, and $u^2 - a^2$ inside the radical.

Using trigonometric substitution, solve integrals involving $a^2 + u^2$ under the radical.

Integrate $\frac{x^3}{\sqrt{16-x^2}}$ using trigonometric substitution.

Evaluate the integral $\displaystyle \int \frac{\sqrt{x^2 - 16}}{x^2} \, dx$ using trigonometric substitution.

Using trigonometric substitution, simplify the expression $\sqrt{a^2 - u^2}$, where $u = a \sin\theta$.