Evaluate \(\int_{-1}^{1} (x+1)\,dx\).
2
Evaluate \(\int_{2}^{3} \frac{1}{x}\,dx\).
\(\log\frac{3}{2}\)
Evaluate \(\int_{1}^{2} (4x^3-5x^2+6x+9)\,dx\).
\(\frac{64}{3}\)
Evaluate \(\int_{0}^{\pi/4} \sin 2x\,dx\).
\(\frac{1}{2}\)
Evaluate \(\int_{0}^{\pi/2} \cos 2x\,dx\).
0
Evaluate \(\int_{4}^{5} e^x\,dx\).
\(e^4(e-1)\)
Evaluate \(\int_{0}^{\pi/4} \tan x\,dx\).
\(\frac{1}{2}\log 2\)
Evaluate \(\int_{\pi/6}^{\pi/4} \cosec x\,dx\).
\(\log\left(\frac{\sqrt{2}-1}{2-\sqrt{3}}\right)\)
Evaluate \(\int_{0}^{1} \frac{dx}{\sqrt{1-x^2}}\).
\(\frac{\pi}{2}\)
Evaluate \(\int_{0}^{1} \frac{dx}{1+x^2}\).
\(\frac{\pi}{4}\)
Evaluate \(\int_{2}^{3} \frac{dx}{x^2-1}\).
\(\frac{1}{2}\log\frac{3}{2}\)
Evaluate \(\int_{0}^{\pi/2} \cos^2 x\,dx\).
\(\frac{\pi}{4}\)
Evaluate \(\int_{2}^{3} \frac{x\,dx}{x^2+1}\).
\(\frac{1}{2}\log 2\)
Evaluate \(\int_{0}^{1} \frac{2x+3}{5x^2+1}\,dx\).
\(\frac{1}{5}\log 6+\frac{3}{\sqrt{5}}\tan^{-1}\sqrt{5}\)
Evaluate \(\int_{0}^{1} x e^{x^2}\,dx\).
\(\frac{1}{2}(e-1)\)
Evaluate \(\int_{1}^{2} \frac{5x^2}{x^2+4x+3}\,dx\).
\(5-\frac{5}{2}\left(9\log\frac{5}{4}-\log\frac{3}{2}\right)\)
Evaluate \(\int_{0}^{\pi/4} (2\sec^2 x+x^3+2)\,dx\).
\(\frac{\pi^4}{1024}+\frac{\pi}{2}+2\)
Evaluate \(\int_{0}^{\pi} \left(\sin^2\frac{x}{2}-\cos^2\frac{x}{2}\right)\,dx\).
0
Evaluate \(\int_{0}^{2} \frac{6x+3}{x^2+4}\,dx\).
\(3\log 2+\frac{3\pi}{8}\)
Evaluate \(\int_{0}^{1} \left(x e^x+\sin\frac{\pi x}{4}\right)\,dx\).
\(1+\frac{4}{\pi}-\frac{2\sqrt{2}}{\pi}\)
\(\int_{1}^{\sqrt{3}} \frac{dx}{1+x^2}\) equals
\(\frac{\pi}{3}\)
\(\frac{2\pi}{3}\)
\(\frac{\pi}{6}\)
\(\frac{\pi}{12}\)
\(\int_{0}^{2/3} \frac{dx}{4+9x^2}\) equals
\(\frac{\pi}{6}\)
\(\frac{\pi}{12}\)
\(\frac{\pi}{24}\)
\(\frac{\pi}{4}\)