Popular Calculus Problems

limit as x approaching 0 of (x^2)/(sin^2(x))	\lim_{x\to\:0}(\frac{x^{2}}{\sin^{2}(x)})
limit as x approaching infinity of e^{-x^2}	\lim_{x\to\:\infty\:}(e^{-x^{2}})
limit as x approaching infinity of sqrt(x^2+1)-x	\lim_{x\to\:\infty\:}(\sqrt{x^{2}+1}-x)
limit as x approaching 7 of (2-sqrt(x-3))/(x^2-49)	\lim_{x\to\:7}(\frac{2-\sqrt{x-3}}{x^{2}-49})
y^{\prime \prime}+y^{\prime}-2y=1-2x^2	y^{\prime\:\prime\:}+y^{\prime\:}-2y=1-2x^{2}
integral of 1/((x+1)^2)	\int\:\frac{1}{(x+1)^{2}}dx
integral of _{1}^2(e^{1/(x^3)})/(x^4)	\int_{1}^{2}\frac{e^{\frac{1}{x^{3}}}}{x^{4}}dx
sum from n=1 to infinity of 1/(n!)	\sum_{n=1}^{\infty\:}\frac{1}{n!}
d/(dx)(1/(1-x))	\frac{d}{dx}(\frac{1}{1-x})
integral of sin^3(x)cos^2(x)	\int\:\sin^{3}(x)\cos^{2}(x)dx
limit as x approaching 0 of xln(x)	\lim_{x\to\:0}(x\ln(x))
2y^{\prime \prime}+7y^{\prime}+3y=0	2y^{\prime\:\prime\:}+7y^{\prime\:}+3y=0
d/(dx)(x^x)	\frac{d}{dx}(x^{x})
integral of e^{-5x}	\int\:e^{-5x}dx
integral of 1/(1-x^2)	\int\:\frac{1}{1-x^{2}}dx
integral from 0 to infinity of e^{-x^2}	\int_{0}^{\infty\:}e^{-x^{2}}dx
integral of 2/x	\int\:\frac{2}{x}dx
integral of sin^2(x)cos(x)	\int\:\sin^{2}(x)\cos(x)dx
dy-(y-1)^2dx=0	dy-(y-1)^{2}dx=0
d/(dx)(sqrt(x))	\frac{d}{dx}(\sqrt{x})
d/(dx)((x^3)/3+1/(4x))	\frac{d}{dx}(\frac{x^{3}}{3}+\frac{1}{4x})
d/(dx)(cos(3x))	\frac{d}{dx}(\cos(3x))
limit as x approaching 4 of (3-sqrt(5+x))/(1-sqrt(5-x))	\lim_{x\to\:4}(\frac{3-\sqrt{5+x}}{1-\sqrt{5-x}})
limit as x approaching 0 of ln(x)	\lim_{x\to\:0}(\ln(x))
y^{\prime \prime}+9y=0	y^{\prime\:\prime\:}+9y=0
d/(dx)(3sin(x))	\frac{d}{dx}(3\sin(x))
integral of 1/(1+e^x)	\int\:\frac{1}{1+e^{x}}dx
integral of 1/(x^2sqrt(x^2-9))	\int\:\frac{1}{x^{2}\sqrt{x^{2}-9}}dx
limit as x approaching 3 of (x^2-9)/(x-3)	\lim_{x\to\:3}(\frac{x^{2}-9}{x-3})
integral of xcos(x)	\int\:x\cos(x)dx
d/(dx)(2sin(x))	\frac{d}{dx}(2\sin(x))
sum from n=1 to infinity of e^{-n}	\sum_{n=1}^{\infty\:}e^{-n}
limit as h approaching 0 of (f(x+h)-f(x))/h	\lim_{h\to\:0}(\frac{f(x+h)-f(x)}{h})
volume y=x^2,x=y^2	volume\:y=x^{2},x=y^{2}
sum from n=1 to infinity of sin(1/n)	\sum_{n=1}^{\infty\:}\sin(\frac{1}{n})
integral of ln(x)^2	\int\:\ln(x)^{2}dx
integral of (sqrt(x))/(sqrt(1-x))	\int\:\frac{\sqrt{x}}{\sqrt{1-x}}dx
integral of 1/(x-1)	\int\:\frac{1}{x-1}dx
integral of 2/(sqrt(x))	\int\:\frac{2}{\sqrt{x}}dx
integral of 5x	\int\:5xdx
d/(dx)(1/(1+x^2))	\frac{d}{dx}(\frac{1}{1+x^{2}})
integral of xln(x+1)	\int\:x\ln(x+1)dx
d/(dx)(x^{3/2})	\frac{d}{dx}(x^{\frac{3}{2}})
integral of 1/(x+1)	\int\:\frac{1}{x+1}dx
derivative cos^2(x)	derivative\:\cos^{2}(x)
limit as x approaching infinity of sqrt(9x^2+x)-3x	\lim_{x\to\:\infty\:}(\sqrt{9x^{2}+x}-3x)
limit as (x,y) approaching (0,0) of (xy)/(sqrt(x^2+y^2))	\lim_{(x,y)\to(0,0)}(\frac{xy}{\sqrt{x^{2}+y^{2}}})
d/(dx)(y)+3y=0	\frac{d}{dx}(y)+3y=0
d/(dx)(3e^x)	\frac{d}{dx}(3e^{x})
integral of sec(x)	\int\:\sec(x)dx
arctan(infinity)	\arctan(\infty)
integral of e	\int\:e
limit as x approaching-3 of (x^2-9)/(x+3)	\lim_{x\to\:-3}(\frac{x^{2}-9}{x+3})
integral of x/(e^x)	\int\:\frac{x}{e^{x}}dx
limit as x approaching infinity of (x!)/(x^x)	\lim_{x\to\:\infty\:}(\frac{x!}{x^{x}})
laplace 0	laplace\:0
sum from n=1 to infinity of (x^n)/(n!)	\sum_{n=1}^{\infty\:}\frac{x^{n}}{n!}
limit as x approaching 0 of (sqrt(x+5)-sqrt(5))/x	\lim_{x\to\:0}(\frac{\sqrt{x+5}-\sqrt{5}}{x})
d/(dx)(e^{-3x})	\frac{d}{dx}(e^{-3x})
integral of _{0}^1sqrt(1-x^2)	\int_{0}^{1}\sqrt{1-x^{2}}dx
integral of 1/(1-x)	\int\:\frac{1}{1-x}dx
integral of e^{-2x}	\int\:e^{-2x}dx
integral of _{0}^2sqrt(4-x^2)	\int_{0}^{2}\sqrt{4-x^{2}}dx
integral of tan(x)	\int\:\tan(x)dx
(infinity)/(infinity)	\frac{\infty\:}{\infty\:}
d/(dx)(xe^{2x})	\frac{d}{dx}(xe^{2x})
integral of 1/(x^2+4)	\int\:\frac{1}{x^{2}+4}dx
integral of (x+1)(3x-2)	\int(x+1)(3x-2)dx
y^{\prime}=x^4-1/x y	y^{\prime\:}=x^{4}-\frac{1}{x}y
integral of tan(2x)	\int\:\tan(2x)dx
1/(infinity)	\frac{1}{\infty\:}
d/(dx)(x+1/x)	\frac{d}{dx}(x+\frac{1}{x})
limit as x approaching infinity of (x/(x+1))^x	\lim_{x\to\:\infty\:}((\frac{x}{x+1})^{x})
integral from 0 to infinity of x^2e^{-x}	\int_{0}^{\infty\:}x^{2}e^{-x}dx
limit as x approaching 0 of (sin(x))/x	\lim_{x\to\:0}(\frac{\sin(x)}{x})
integral of 0	\int\:0dx
integral of (x^3)/((x^2+4)^{3/2)}	\int\:\frac{x^{3}}{(x^{2}+4)^{\frac{3}{2}}}dx
limit as x approaching 1 of (x-1)/(x^2-1)	\lim_{x\to\:1}(\frac{x-1}{x^{2}-1})
d/(dx)(cos(2x))	\frac{d}{dx}(\cos(2x))
∂/(∂y)(sqrt(x^2+y^2))	\frac{∂}{∂y}(\sqrt{x^{2}+y^{2}})
integral of 1/(1+x)	\int\:\frac{1}{1+x}dx
cos(infinity)	\cos(\infty)
integral of-e^{-x}	\int\:-e^{-x}dx
laplace sin(2t)	laplace\:\sin(2t)
limit as x approaching infinity of x^{1/x}	\lim_{x\to\:\infty\:}(x^{\frac{1}{x}})
integral of x/2	\int\:\frac{x}{2}dx
limit as x approaching 0 of 1/(xsqrt(1+x))-1/x	\lim_{x\to\:0}(\frac{1}{x\sqrt{1+x}}-\frac{1}{x})
limit as x approaching infinity of 2^x	\lim_{x\to\:\infty\:}(2^{x})
integral of _{1}^2(e^{1/(x^5)})/(x^6)	\int_{1}^{2}\frac{e^{\frac{1}{x^{5}}}}{x^{6}}dx
d/(dx)(3/(x^2))	\frac{d}{dx}(\frac{3}{x^{2}})
integral of (sin(2x))/(1+cos^2(x))	\int\:\frac{\sin(2x)}{1+\cos^{2}(x)}dx
inverselaplace 1	inverselaplace\:1
integral of x^3sqrt(x^2+1)	\int\:x^{3}\sqrt{x^{2}+1}dx
integral of e^{3x}	\int\:e^{3x}dx
integral of (sqrt(1+x^2))/x	\int\:\frac{\sqrt{1+x^{2}}}{x}dx
d/(dx)((x+1)/(x-1))	\frac{d}{dx}(\frac{x+1}{x-1})
limit as x approaching infinity of ln(1/x)	\lim_{x\to\:\infty\:}(\ln(\frac{1}{x}))
integral of x/(x+1)	\int\:\frac{x}{x+1}dx
d/(dx)(1/(2sqrt(x)))	\frac{d}{dx}(\frac{1}{2\sqrt{x}})
d/(dx)(e^{3x}(-2sin(2x)+3cos(2x)))	\frac{d}{dx}(e^{3x}(-2\sin(2x)+3\cos(2x)))

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