10 Questions
What is the value of the integral $\int \sec^2 \sqrt{x} \sqrt{x} dx$?
$\frac{4}{3} \sqrt{x}^3 + C$
Evaluate the integral $\int 2 e^{1/x} dx$.
$-2e^{1/x} + C$
What is the value of the integral $\int \frac{3}{x} dx$?
$3 \ln |x| + C$
Evaluate the integral $\int \sqrt{x} \sqrt{4 - x} dx$.
$\frac{2}{3}(4 - x)^{3/2} + C$
What is the value of the integral $\int x e^{-x} \cos x dx$?
$\frac{1}{2} e^{-x} (\cos x + x \sin x) + C$
Evaluate the integral $\int \sin^4 x \cos x dx$.
$-\frac{1}{5} \sin^5 x + C$
What is the value of the integral $\int \frac{dx}{\cos^2 x \tan x}$?
$-\cot x + C$
Evaluate the integral $\int \frac{dx}{9 + \sin^4 4x}$.
$\frac{1}{8} \tan^{-1} \left(\frac{\sin 4x}{3}\right) + C$
What is the value of the integral $\int \frac{x}{e^x + 4} dx$?
$-\frac{1}{2} \ln(e^x + 4) + C$
Evaluate the integral $\int \frac{x}{(e^x + 4)^4} dx$.
$-\frac{1}{12} \frac{1}{(e^x + 4)^3} + C$
Test your knowledge of integration by partial fractions with this quiz for a Spring 2024 Integral Calculus class. Evaluate various integrals involving fractions and explore different techniques in calculus.
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