Just the Basics
\int\ x\ dx
What is
\frac{1}{2}x^2+C
int\ sqrt(2x+1)\ dx
What is
1/3 (2x+1)^(3/2)+C
int\ cot x\ dx
What is
ln|sin x|+C
int\ 1/(1+x^2)dx
What is
tan^-1 x+C
int_-5^-1 1/xdx
What is
-ln5
int\ sin^-1 x\ dx
What is
x sin^-1 x+sqrt(1 - x^2)+C
\int\ \sin x\ dx
What is
-cos x+C
int\ x cos(x^2)dx
What is
1/2 sin(x^2)+C
int\ cos^3 x\ dx
What is
sin x-1/3 sin^3 x+C
int x/(1+x^2)dx
What is
1/2ln|1+x^2|+C
int_0^(pi/2) e^(sin x)cos x\ dx
What is
e-1
int\ (x ln x)^-1 dx
What is
ln|ln x|+C
int\ 1/xdx
What is
ln|x|+C
int\ x\cos(x)dx
What is
x sin x+cos x+C
int\ sec^3 x tan^3 x\ dx
What is
1/5 sec^5 x-1/3 sec^3 x+C
int\ (1+x^2)/xdx
What is
ln|x|+1/2x^2+C
int_1^e x ln x\ dx
What is
1/4(1+e^2)
int\ e^sqrt(x)dx
What is
2sqrt x*e^sqrt x-2e^sqrt x+C
int\ 1/(x sqrt(x^2-1)) dx
What is
sec^-1 x+C
int\ x^2 ln x\ dx
What is
1/3 x^3 ln x-1/9 x^3+C
int\ 1/sqrt(25-9x^2)dx
What is
1/3 sin^-1 (3/5 x)+C
int\ x^2/(1+x^2)dx
What is
x-tan^-1 x+C
int_0^2 sqrt(4-x^2)\ dx
What is
pi
int\ x/(x^4+9)dx
What is
1/6 tan^-1 (x^2/3)+C
int\ 2^x dx
What is
(2^x)/ln 2+C
int\ x^2 e^x dx
What is
x^2 e^x-2x e^x+2 e^x+C
int\ e^x cos x\ dx
What is
1/2 e^x sin x + 1/2 e^x cos x + C
int\ 1/(1-x^2)dx
What is
1/2 ln|1+x|-1/2 ln|1-x|+C
int_1^2 1/(x^2(x-3))dx
What is
-1/6-2/9 ln 2
int\ (sin x)/(cos x+cos^2 x)dx
What is
ln|1+cos x|-ln|cos x|+C