Calculus 2: Trigonometric Integrals

$\displaystyle \int cos^3x \, dx$

$\displaystyle \int sin^2x\, dx$

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

$\displaystyle \int sin^3x \, cos^4x ,\ dx$

Evaluate $\displaystyle \int \frac{x \, sin^{-1}x}{\sqrt{1-x^2}} \, dx$

Evaluate$\displaystyle \int e^{cos^{-1}x}\, dx$

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

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

Evaluate the integral $\displaystyle \int_{0}^{\pi/2} \frac{\cos t}{\sqrt{1 + \sin^2 t}} \, dt$.

Evaluate $\displaystyle \int \cos^2(\theta) \, d\theta$ using the double angle identity.

Evaluate the integral of $\frac{1}{\sqrt{1-x^2}}$ which is equivalent to the inverse sine of x.

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 integral of cosine of $z$ over the square root of $3 + \cos^2(z) \, dz$.

Using trigonometric identities, such as $\cos^2(\theta) + \sin^2(\theta) = 1$, find related identities to simplify expressions in integral problems.

Calculate the definite integral of $\sec^2(\theta) - 1$ from $\theta = 0$ to $\theta = \frac{\pi}{6}$.

Integrate $\cos^3 \theta$ with respect to $\theta$.

Find the anti-derivative of $\cos^3(x)$.

Find the anti-derivative of $\cos^5(x)$.