Calculus 2

$\displaystyle \int cos^4(5x)\, dx$

The first-quadrant area is bounded by the curve $y^2 = 4x$, the x axis, and the line x = 4 is rotated about the y axis. Find the volume generated: (a) By the ring method (b) By the shell method

$\displaystyle \int \frac{tan^3x}{sec^2x} \, dx$

Evaluate $\int x^2 \, cos(x) \, dx$

Use the disk method to find the volume of the solid of rotation by rotating the bounded area around the y-axis

$y = 2x^2$, $y = 0$, $x = 2$

$\displaystyle \int tan^3x \, sec^3x \, dx$

Compute $\int xe^{5x}dx$ and $\displaystyle \int_{\pi/4}^{\pi/3} cos(x) ln(sin(x)) \, dx$

Given $x^3 = y^5 + 2$, find the arc length from $y = 1$ to $y = 3$ and the surface area when the arc is rotated about the x-axis.

Integrate $\frac{\sqrt{9-x^2}}{x^2} \, dx$ using trigonometric substitution.

Integrate $\frac{1}{x^2 \sqrt{x^2 + 4}} \, dx$ using trigonometric substitution.

Simplify and integrate the expression $(x^2 + 9)^{3/2}$ using trigonometric substitution where $x = 3\tan(\theta)$.

Evaluate the integral $\displaystyle \int \frac{dt}{t^2 + 9}$ using trigonometric substitution.

Integrate $1 \over \sqrt{a^2 - x^2}$.

Integrate the square root of $2-x^2$ over $x^2$.

Integrate the square root of $1 - 4x^2$.

Integrate $\displaystyle \frac{1}{x \sqrt{9-x^2}}$.

Integrate $\frac{\sqrt{4-x^2}}{x^2}$ using trigonometric substitution.

Find the indefinite integral of $\displaystyle \int \frac{x^3}{\sqrt{x^2 + 9}} \, dx$ using trigonometric substitution.

Perform the substitution $u = x + 1$ and express the integral $\displaystyle \int \sqrt{1 - (x + 1)^2}^5 \, dx$ in terms of $u$.

Perform the trigonometric substitution for the integral involving $\sqrt{1 + x^2}$.