Calculus I Limits and Derivatives

Use the inspection method to find the general antiderivative: \(\int (6x^2 - 4x + 5) \, dx\)

Evaluate using substitution: \(\int 2x e^{x^2} \, dx\)

By inspection, find the antiderivative of \(f(x) = \sec^2(x) + \sin(x)\text{.}\)

Find \(\int \cos(3x) \, dx\text{.}\)

Evaluate \(\int \frac{(\ln x)^2}{x} \, dx\) using \(u = \ln x\text{.}\)

Find the antiderivative: \(\int 2x(x^2 + 5)^4 \, dx\)

Find \(\int e^{\sin(x)} \cos(x) \, dx\)

Evaluate \(\int \frac{\ln(x)}{x} \, dx\)

Find \(\int x \sqrt{x^2 + 1} \, dx\)

Evaluate \(\int \cos(3x) \, dx\)

Evaluate \(\int \frac{1}{(x-1)(x+2)} \, dx\)

Find \(\int \frac{x+5}{x^2+x-2} \, dx\)

Evaluate \(\int \frac{1}{x^2-4} \, dx\)

Find \(\int \frac{2x}{(x+1)^2} \, dx\)

Evaluate \(\int \frac{1}{x^2+x} \, dx\)

Find \(\int x e^x \, dx\)

Evaluate \(\int x \sin(x) \, dx\)

Find \(\int \ln(x) \, dx\)

Evaluate \(\int x^2 \ln(x) \, dx\)

Find \(\int \arctan(x) \, dx\)

Use integration by parts to evaluate: \(\int x e^x \, dx\)

Evaluate the following antiderivative: \(\int \ln(x) \, dx\)

Use partial fraction decomposition to find: \(\int \frac{1}{x^2 - 1} \, dx\)

What is the correct form of the partial fraction decomposition for the integrand \(\frac{5x}{(x-2)(x^2+1)}\text{?}\)

Evaluate using integration by parts: \(\int x \cos(x) \, dx\)