Find an anti derivative (or integral) of \(\sin 2x\) by the method of inspection.
\(-\frac{1}{2}\cos 2x\)
Find an anti derivative (or integral) of \(\cos 3x\) by the method of inspection.
\(\frac{1}{3}\sin 3x\)
Find an anti derivative (or integral) of \(e^{2x}\) by the method of inspection.
\(\frac{1}{2}e^{2x}\)
Find an anti derivative (or integral) of \((ax + b)^2\) by the method of inspection.
\(\frac{1}{3a}(ax + b)^3\)
Find an anti derivative (or integral) of \(\sin 2x - 4e^{3x}\) by the method of inspection.
\(-\frac{1}{2}\cos 2x - \frac{4}{3}e^{3x}\)
Evaluate the integral \(\int (4e^{3x} + 1)\,dx\).
\(\frac{4}{3}e^{3x} + x + C\)
Evaluate the integral \(\int x^2\left(1 - \frac{1}{x^2}\right)dx\).
\(\frac{x^3}{3} - x + C\)
Evaluate the integral \(\int (ax^2 + bx + c)\,dx\).
\(\frac{ax^3}{3} + \frac{bx^2}{2} + cx + C\)
Evaluate the integral \(\int (2x^2 + e^x)\,dx\).
\(\frac{2}{3}x^3 + e^x + C\)
Evaluate the integral \(\int \left(\sqrt{x} - \frac{1}{\sqrt{x}}\right)^2 dx\).
\(\frac{x^2}{2} + \log|x| - 2x + C\)
Evaluate the integral \(\int \frac{x^3 + 5x^2 - 4}{x^2} dx\).
\(\frac{x^2}{2} + 5x + \frac{4}{x} + C\)
Evaluate the integral \(\int \frac{x^3 + 3x + 4}{\sqrt{x}} dx\).
\(\frac{2}{7}x^{7/2} + 2x^{3/2} + 8\sqrt{x} + C\)
Evaluate the integral \(\int \frac{x^3 - x^2 + x - 1}{x - 1} dx\).
\(\frac{x^3}{3} + x + C\)
Evaluate the integral \(\int (1 - x)\sqrt{x}\,dx\).
\(\frac{2}{3}x^{3/2} - \frac{2}{5}x^{5/2} + C\)
Evaluate the integral \(\int \sqrt{x}(3x^2 + 2x + 3)\,dx\).
\(\frac{6}{7}x^{7/2} + \frac{4}{5}x^{5/2} + 2x^{3/2} + C\)
Evaluate the integral \(\int (2x - 3\cos x + e^x)\,dx\).
\(x^2 - 3\sin x + e^x + C\)
Evaluate the integral \(\int (2x^2 - 3\sin x + 5\sqrt{x})\,dx\).
\(\frac{2}{3}x^3 + 3\cos x + \frac{10}{3}x^{3/2} + C\)
Evaluate the integral \(\int \sec x(\sec x + \tan x)\,dx\).
\(\tan x + \sec x + C\)
Evaluate the integral \(\int \frac{\sec^2 x}{\cosec^2 x}\,dx\).
\(\tan x - x + C\)
Evaluate the integral \(\int \frac{2 - 3\sin x}{\cos^2 x}\,dx\).
\(2\tan x - 3\sec x + C\)
The anti derivative of \(\left(\sqrt{x} + \frac{1}{\sqrt{x}}\right)\) equals
\(\frac{1}{3}x^{1/3} + 2x^{1/2} + C\)
\(\frac{2}{3}x^{2/3} + \frac{1}{2}x^2 + C\)
\(\frac{2}{3}x^{3/2} + 2x^{1/2} + C\)
\(\frac{3}{2}x^{3/2} + \frac{1}{2}x^{1/2} + C\)
If \(\frac{d}{dx}f(x) = 4x^3 - \frac{3}{x^4}\) such that \(f(2) = 0\), then \(f(x)\) is
\(x^4 + \frac{1}{x^3} - \frac{129}{8}\)
\(x^3 + \frac{1}{x^4} + \frac{129}{8}\)
\(x^4 + \frac{1}{x^3} + \frac{129}{8}\)
\(x^3 + \frac{1}{x^4} - \frac{129}{8}\)