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Popular Calculus Problems

integral of (x+sqrt(1+x^2))^6	\int\:(x+\sqrt{1+x^{2}})^{6}dx
limit as x approaches 2 of sin((pix)/2)	\lim\:_{x\to\:2}(\sin(\frac{pix}{2}))
derivative of (r^6-9r)e^r	derivative\:(r^{6}-9r)e^{r}
integral of (8sqrt(x))/(x-1)	\int\:\frac{8\sqrt{x}}{x-1}dx
f(x)=6x^3	f(x)=6x^{3}
d/(dz)(z/((z^2+R^2)^{3/2)})	\frac{d}{dz}(\frac{z}{(z^{2}+R^{2})^{\frac{3}{2}}})
integral of 0/x	\int\:\frac{0}{x}dx
derivative of (e^x/(x^7))	\frac{d}{dx}(\frac{e^{x}}{x^{7}})
integral of a^{5x}	\int\:a^{5x}dx
integral from 0 to pi/2 of 2-sin(x)	\int\:_{0}^{\frac{π}{2}}2-\sin(x)dx
(d^2)/(dx^2)(x(1+x^2)^{10})	\frac{d^{2}}{dx^{2}}(x(1+x^{2})^{10})
derivative of 3x^{-5}	derivative\:3x^{-5}
(\partial)/(\partial v)(usin(v))	\frac{\partial\:}{\partial\:v}(u\sin(v))
limit as x approaches pi of sec(x)	\lim\:_{x\to\:π}(\sec(x))
integral of ((2x+4))/(x^2+5x-6)	\int\:\frac{(2x+4)}{x^{2}+5x-6}dx
derivative of cos(ln(3x))	\frac{d}{dx}(\cos(\ln(3x)))
integral of sqrt(x)-x	\int\:\sqrt{x}-xdx
area 2-x^2,-x	area\:2-x^{2},-x
limit as x approaches-1 of 4x^2	\lim\:_{x\to\:-1}(4x^{2})
(\partial)/(\partial x)(4x^2e^{ay}+3e^{bx})	\frac{\partial\:}{\partial\:x}(4x^{2}e^{ay}+3e^{bx})
integral of (tan^3(x))/(cos^3(x))	\int\:\frac{\tan^{3}(x)}{\cos^{3}(x)}dx
integral of sin(cos(x))sin(x)	\int\:\sin(\cos(x))\sin(x)dx
derivative of 7/(x-3)	\frac{d}{dx}(\frac{7}{x-3})
derivative of-3cos(3x)	derivative\:-3\cos(3x)
derivative of f(x)=(x^2)/(x^3+1)	derivative\:f(x)=\frac{x^{2}}{x^{3}+1}
integral from 2 to 7 of 1/(sqrt(x-2))	\int\:_{2}^{7}\frac{1}{\sqrt{x-2}}dx
derivative of f(x)=e^{4xsin(2x)}	derivative\:f(x)=e^{4x\sin(2x)}
(\partial)/(\partial x)((e^x)/(u(x)+x^2))	\frac{\partial\:}{\partial\:x}(\frac{e^{x}}{u(x)+x^{2}})
y^{''}-9/x y^'+(34)/(x^2)y=0	y^{\prime\:\prime\:}-\frac{9}{x}y^{\prime\:}+\frac{34}{x^{2}}y=0
(dy)/(dx)=5y+2	\frac{dy}{dx}=5y+2
derivative of (6x+2x^2)/((3+2x)^2)	derivative\:\frac{6x+2x^{2}}{(3+2x)^{2}}
integral of (x+1)/(sqrt(x^2-9))	\int\:\frac{x+1}{\sqrt{x^{2}-9}}dx
(\partial)/(\partial x)(-3x^2y^3sin(x^3y^3))	\frac{\partial\:}{\partial\:x}(-3x^{2}y^{3}\sin(x^{3}y^{3}))
derivative of f(0)= x/(x^2+1)	derivative\:f(0)=\frac{x}{x^{2}+1}
(\partial)/(\partial y)(2x-3yz)	\frac{\partial\:}{\partial\:y}(2x-3yz)
d/(d{r)}((200{r}({r}+2))/((2+3{r))^2})	\frac{d}{d{r}}(\frac{200{r}({r}+2)}{(2+3{r})^{2}})
tangent of y=sqrt(9-10x),\at x=-1	tangent\:y=\sqrt{9-10x},\at\:x=-1
derivative of 2xy^3	\frac{d}{dx}(2xy^{3})
(\partial)/(\partial y)(e^{sin(x+y)})	\frac{\partial\:}{\partial\:y}(e^{\sin(x+y)})
tangent of f(x)=1+4csc(x),\at x=-pi/3	tangent\:f(x)=1+4\csc(x),\at\:x=-\frac{π}{3}
sum from n=1 to infinity of 2/(3n+10)	\sum\:_{n=1}^{\infty\:}\frac{2}{3n+10}
integral from 1 to 2 of 4xsqrt(4x^2+4)	\int\:_{1}^{2}4x\sqrt{4x^{2}+4}dx
integral of (3x^4-5x^2+6x)	\int\:(3x^{4}-5x^{2}+6x)dx
sum from n=1 to infinity of 8	\sum\:_{n=1}^{\infty\:}8
(\partial)/(\partial v)(u^2+v^2)	\frac{\partial\:}{\partial\:v}(u^{2}+v^{2})
integral of 1/(5+2x)	\int\:\frac{1}{5+2x}dx
tangent of (x^2+1)^{(x+1)}	tangent\:(x^{2}+1)^{(x+1)}
derivative of (2x+5/3)	\frac{d}{dx}(\frac{2x+5}{3})
f(x)=xarctan(x)	f(x)=x\arctan(x)
limit as x approaches 0 of 1/(x^{2/3)}	\lim\:_{x\to\:0}(\frac{1}{x^{\frac{2}{3}}})
integral of (4x^3+7)	\int\:(4x^{3}+7)dx
(\partial)/(\partial x)(zsin(x)+y^2)	\frac{\partial\:}{\partial\:x}(z\sin(x)+y^{2})
integral of x/((x+2)^{2/3)}	\int\:\frac{x}{(x+2)^{\frac{2}{3}}}dx
limit as x approaches 0 of cos(pi/2)	\lim\:_{x\to\:0}(\cos(\frac{π}{2}))
derivative of y=8e^xcos(x)	derivative\:y=8e^{x}\cos(x)
integral of ((x+1))/x	\int\:\frac{(x+1)}{x}dx
y^'=x+y,y(0)=7	y^{\prime\:}=x+y,y(0)=7
derivative of 2x^{-2}	\frac{d}{dx}(2x^{-2})
y^{''}-8y^'+20y=0	y^{\prime\:\prime\:}-8y^{\prime\:}+20y=0
integral from 1 to sqrt(2 of)x5^{(x^2)}	\int\:_{1}^{\sqrt{2}}x5^{(x^{2})}dx
limit as x approaches 0 of (3x^2-2x)/x	\lim\:_{x\to\:0}(\frac{3x^{2}-2x}{x})
integral of (e^{2x}-6e^x)/(e^{2x)+11}	\int\:\frac{e^{2x}-6e^{x}}{e^{2x}+11}dx
tangent of f(x)=sqrt(20x+5)	tangent\:f(x)=\sqrt{20x+5}
integral of (e^{1/(x^4)})/(x^5)	\int\:\frac{e^{\frac{1}{x^{4}}}}{x^{5}}dx
limit as x approaches 2 of (4x-3)/(x+2)	\lim\:_{x\to\:2}(\frac{4x-3}{x+2})
((x^4)/4)^'	(\frac{x^{4}}{4})^{\prime\:}
inverse oflaplace (360)/(2s^2+10s+8)	inverselaplace\:\frac{360}{2s^{2}+10s+8}
(\partial)/(\partial x)(ye^{3x}*3)	\frac{\partial\:}{\partial\:x}(ye^{3x}\cdot\:3)
tangent of y= 7/(x^2+3),(2,1)	tangent\:y=\frac{7}{x^{2}+3},(2,1)
limit as x approaches 2 of x^3+4x^2-3x-6	\lim\:_{x\to\:2}(x^{3}+4x^{2}-3x-6)
integral of 1/(t^2sqrt(5-t^2))	\int\:\frac{1}{t^{2}\sqrt{5-t^{2}}}dt
integral from 1 to 4 of 3/(x^2)	\int\:_{1}^{4}\frac{3}{x^{2}}dx
(\partial)/(\partial x)(x+y+xy+x/y+y/x)	\frac{\partial\:}{\partial\:x}(x+y+xy+\frac{x}{y}+\frac{y}{x})
y^{''}+y=k	y^{\prime\:\prime\:}+y=k
integral from 4 to 5 of x^2sqrt(x-4)	\int\:_{4}^{5}x^{2}\sqrt{x-4}dx
(\partial)/(\partial t)((8.31t)/(V(t)))	\frac{\partial\:}{\partial\:t}(\frac{8.31t}{V(t)})
limit as x approaches 2 of (2x-6)/(x-1)	\lim\:_{x\to\:2}(\frac{2x-6}{x-1})
limit as x approaches 9-of (5x)/(x-9)	\lim\:_{x\to\:9-}(\frac{5x}{x-9})
derivative of-4x^4+8x^3	\frac{d}{dx}(-4x^{4}+8x^{3})
inverse oflaplace ((3s+1))/(s(s+2))	inverselaplace\:\frac{(3s+1)}{s(s+2)}
y^'-6/x y=((y^5))/(x^{18)},y(1)=1	y^{\prime\:}-\frac{6}{x}y=\frac{(y^{5})}{x^{18}},y(1)=1
derivative of g(x)=3(5-7x)^5	derivative\:g(x)=3(5-7x)^{5}
derivative of sin(pi/4)	\frac{d}{dx}(\sin(\frac{π}{4}))
integral of (7e^{2t})/(1+e^{4t)}	\int\:\frac{7e^{2t}}{1+e^{4t}}dt
derivative of x^3-2x+4	\frac{d}{dx}(x^{3}-2x+4)
limit as x approaches 1 of (x^2-1)/(x-3)	\lim\:_{x\to\:1}(\frac{x^{2}-1}{x-3})
laplacetransform cos(ax+b)	laplacetransform\:\cos(ax+b)
integral of 5(1-x)^4	\int\:5(1-x)^{4}dx
integral of (24)/(x^3)	\int\:\frac{24}{x^{3}}dx
limit as x approaches 1 of (x-3)/(x^2+4)	\lim\:_{x\to\:1}(\frac{x-3}{x^{2}+4})
(dy)/(dx)=x+y,y(0)=3	\frac{dy}{dx}=x+y,y(0)=3
integral from 1 to sqrt(3 of)arctan(x)	\int\:_{1}^{\sqrt{3}}\arctan(x)dx
integral of (x+1)/(x^2+16)	\int\:\frac{x+1}{x^{2}+16}dx
derivative of f(x)=sqrt(x)(x-4)	derivative\:f(x)=\sqrt{x}(x-4)
derivative of-2xe^{-2x}	\frac{d}{dx}(-2xe^{-2x})
integral of (x^2+x-1)/(x^3+2x^2+x)	\int\:\frac{x^{2}+x-1}{x^{3}+2x^{2}+x}dx
integral of 1/(sqrt(x^2+y^2))	\int\:\frac{1}{\sqrt{x^{2}+y^{2}}}dx
tangent of f(x)=x^4+9x^2-x,\at x=1	tangent\:f(x)=x^{4}+9x^{2}-x,\at\:x=1
sum from n=3 to infinity of (4/7)^n	\sum\:_{n=3}^{\infty\:}(\frac{4}{7})^{n}
integral of 1/(cos^2(4x))	\int\:\frac{1}{\cos^{2}(4x)}dx

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