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Popular Calculus Problems

derivative of 22(2e^{x^2}x^2+e^{x^2})	\frac{d}{dx}(22(2e^{x^{2}}x^{2}+e^{x^{2}}))
integral of (2sin(x)-3cos(x)+12)	\int\:(2\sin(x)-3\cos(x)+12)dx
derivative of (1+x^{-1})^2	derivative\:(1+x^{-1})^{2}
integral of 1/(x^2)sqrt(3+1/x)	\int\:\frac{1}{x^{2}}\sqrt{3+\frac{1}{x}}dx
derivative of sin(ln(2x))	\frac{d}{dx}(\sin(\ln(2x)))
(d^2)/(dx^2)(1/(2+t))	\frac{d^{2}}{dx^{2}}(\frac{1}{2+t})
integral of (e^{x^2})/(x^2)	\int\:\frac{e^{x^{2}}}{x^{2}}dx
derivative of-cos^3(x)	\frac{d}{dx}(-\cos^{3}(x))
integral from 0 to pi of 5sin^2(xco)s^4x	\int\:_{0}^{π}5\sin^{2}(xco)s^{4}xdx
derivative of e^xcot(y+2ycsc(y))	\frac{d}{dx}(e^{x}\cot(y)+2y\csc(y))
integral of 1/(2(x-2))	\int\:\frac{1}{2(x-2)}dx
integral from 0 to 1 of x^2e^{x^3-1}	\int\:_{0}^{1}x^{2}e^{x^{3}-1}dx
(\partial)/(\partial x)(x^2+y^3+w^4)	\frac{\partial\:}{\partial\:x}(x^{2}+y^{3}+w^{4})
area y=\|3x\|,y=x^2-4	area\:y=\left\|3x\right\|,y=x^{2}-4
integral of 1/(1-4x)	\int\:\frac{1}{1-4x}dx
limit as x approaches-1 of (x^2+5)/(x+6)	\lim\:_{x\to\:-1}(\frac{x^{2}+5}{x+6})
derivative of (2x+3)^{1.4}	derivative\:(2x+3)^{1.4}
derivative of (2x^2+1)(x-3)^2	derivative\:(2x^{2}+1)(x-3)^{2}
integral of 8sin^3(x)	\int\:8\sin^{3}(x)dx
4xydx+(x^2+1)dy=0	4xydx+(x^{2}+1)dy=0
inverse oflaplace ((s+1))/(s^2)	inverselaplace\:\frac{(s+1)}{s^{2}}
(\partial)/(\partial x)(8e^{x-y})	\frac{\partial\:}{\partial\:x}(8e^{x-y})
(\partial)/(\partial x)(e^{x^2+y})	\frac{\partial\:}{\partial\:x}(e^{x^{2}+y})
integral of 5sin^3(xco)s^2x	\int\:5\sin^{3}(xco)s^{2}xdx
(dy)/(dx)= y/x+csc(y/x)	\frac{dy}{dx}=\frac{y}{x}+\csc(\frac{y}{x})
derivative of-2sin(x^2)-4x^2cos(x^2)	derivative\:-2\sin(x^{2})-4x^{2}\cos(x^{2})
derivative of f(x)=(x^2+3x+1)(2x+3)	derivative\:f(x)=(x^{2}+3x+1)(2x+3)
integral of (2x)/((x-2)(x+1))	\int\:\frac{2x}{(x-2)(x+1)}dx
area y= 5/x ,y= 5/(x^2),x=4	area\:y=\frac{5}{x},y=\frac{5}{x^{2}},x=4
derivative of (10\sqrt[3]{z})/(z^2)	derivative\:\frac{10\sqrt[3]{z}}{z^{2}}
derivative of Ae^{3x}*3	\frac{d}{dx}(Ae^{3x}\cdot\:3)
limit as x approaches 0 of x(11+4/x)	\lim\:_{x\to\:0}(x(11+\frac{4}{x}))
integral of cos((npi)/2 x)	\int\:\cos(\frac{nπ}{2}x)dx
limit as x approaches 1 of sin(1/x)	\lim\:_{x\to\:1}(\sin(\frac{1}{x}))
integral of (x^2*sin(x))	\int\:(x^{2}\cdot\:\sin(x))dx
derivative of x^{2/3}+y^{2/3}	\frac{d}{dx}(x^{\frac{2}{3}}+y^{\frac{2}{3}})
derivative of-tan(x^2)	\frac{d}{dx}(-\tan(x^{2}))
integral of 1/(ln(x^2))	\int\:\frac{1}{\ln(x^{2})}dx
sum from n=1 to infinity of (3^n)/(5^n)	\sum\:_{n=1}^{\infty\:}\frac{3^{n}}{5^{n}}
limit as x approaches 0 of (9+x)/(x^3)	\lim\:_{x\to\:0}(\frac{9+x}{x^{3}})
(\partial)/(\partial x)((2x^2-5x)^3(2x+1))	\frac{\partial\:}{\partial\:x}((2x^{2}-5x)^{3}(2x+1))
integral from 0 to 27 of \sqrt[3]{x}	\int\:_{0}^{27}\sqrt[3]{x}dx
limit as s approaches infinity of ct	\lim\:_{s\to\:\infty\:}(ct)
area x=sqrt(y),x=2,y=0	area\:x=\sqrt{y},x=2,y=0
(dy)/(dx)= 1/(sqrt(1-x^2))	\frac{dy}{dx}=\frac{1}{\sqrt{1-x^{2}}}
derivative of 2/(\sqrt[3]{x}+3cos(x))	\frac{d}{dx}(\frac{2}{\sqrt[3]{x}}+3\cos(x))
integral from 0 to 1 of (26)/(4y-1)	\int\:_{0}^{1}\frac{26}{4y-1}dy
integral of (sec^2(x)tan(x))	\int\:(\sec^{2}(x)\tan(x))dx
integral of x^5sqrt(12+x^6)	\int\:x^{5}\sqrt{12+x^{6}}dx
integral of x^9	\int\:x^{9}dx
area x^3,x,-1,1	area\:x^{3},x,-1,1
derivative of (x^4+2x^2)/(x^2)	derivative\:\frac{x^{4}+2x^{2}}{x^{2}}
integral of e^x(x^2-5x)	\int\:e^{x}(x^{2}-5x)dx
(dy)/(dx)=(x^3)/(y^2)	\frac{dy}{dx}=\frac{x^{3}}{y^{2}}
integral of (1-cos(2x))^2	\int\:(1-\cos(2x))^{2}dx
(d^3)/(dx^3)(1/(sqrt(x)))	\frac{d^{3}}{dx^{3}}(\frac{1}{\sqrt{x}})
integral of (5x^2+6+7/(x^2+1))	\int\:(5x^{2}+6+\frac{7}{x^{2}+1})dx
tangent of f(x)= 9/(x^2),\at x=a	tangent\:f(x)=\frac{9}{x^{2}},\at\:x=a
sum from n=2 to infinity of 1/(sqrt(n*(n+1)))	\sum\:_{n=2}^{\infty\:}\frac{1}{\sqrt{n\cdot\:(n+1)}}
derivative of f(x)=x^2(x^2-8)	derivative\:f(x)=x^{2}(x^{2}-8)
(\partial)/(\partial y)(e^{3x}cos(8y))	\frac{\partial\:}{\partial\:y}(e^{3x}\cos(8y))
integral of e^{-t}	\int\:e^{-t}dt
integral of (1+cos(x))/(sin(x))	\int\:\frac{1+\cos(x)}{\sin(x)}dx
limit as x approaches 2 of 3/(x+1)	\lim\:_{x\to\:2}(\frac{3}{x+1})
integral of (2x-5)^{-1/2}	\int\:(2x-5)^{-\frac{1}{2}}dx
(\partial)/(\partial x)(yx^3)	\frac{\partial\:}{\partial\:x}(yx^{3})
f(x)=(x^3+7)/x	f(x)=\frac{x^{3}+7}{x}
derivative of y=x^{e^x}	derivative\:y=x^{e^{x}}
integral of xsin(1/9 x)	\int\:x\sin(\frac{1}{9}x)dx
integral from-4 to 4 of x(16-x^2)	\int\:_{-4}^{4}x(16-x^{2})dx
limit as x approaches 6 of sqrt(5x+6)	\lim\:_{x\to\:6}(\sqrt{5x+6})
derivative of e^{x-1}-ln(x-(x-1)^2-1)	\frac{d}{dx}(e^{x-1}-\ln(x)-(x-1)^{2}-1)
integral from 1 to 2 of 5sqrt(4x^2-3)	\int\:_{1}^{2}5\sqrt{4x^{2}-3}dx
(1/(t-1))^'	(\frac{1}{t-1})^{\prime\:}
integral of x/((7x^2+3)^5)	\int\:\frac{x}{(7x^{2}+3)^{5}}dx
y^{'''}+49y^'=0	y^{\prime\:\prime\:\prime\:}+49y^{\prime\:}=0
tangent of e^{x^5}	tangent\:e^{x^{5}}
derivative of sqrt(8x^2+7)	\frac{d}{dx}(\sqrt{8x^{2}+7})
integral from 0 to 2 of 3^{-x}	\int\:_{0}^{2}3^{-x}dx
y^{''}-2y^'+10y=e^xcos(3x)	y^{\prime\:\prime\:}-2y^{\prime\:}+10y=e^{x}\cos(3x)
integral of sin(u^2)	\int\:\sin(u^{2})du
(\partial)/(\partial y)((2y)/(x^2+y^2))	\frac{\partial\:}{\partial\:y}(\frac{2y}{x^{2}+y^{2}})
derivative of (x^2)/(8+sqrt(x))	derivative\:\frac{x^{2}}{8+\sqrt{x}}
integral of (cos(x))/(sqrt(sin(x)))	\int\:\frac{\cos(x)}{\sqrt{\sin(x)}}dx
sum from n=0 to infinity of 1/n-1/(n+2)	\sum\:_{n=0}^{\infty\:}\frac{1}{n}-\frac{1}{n+2}
y^'=-1.5y	y^{\prime\:}=-1.5y
integral of cos^4(x/2)	\int\:\cos^{4}(\frac{x}{2})dx
laplacetransform 2t^2	laplacetransform\:2t^{2}
integral from 0 to 9 of (sqrt(9-y)+2)^2	\int\:_{0}^{9}(\sqrt{9-y}+2)^{2}dy
9xy^'=2xe^x-9y+6x^2	9xy^{\prime\:}=2xe^{x}-9y+6x^{2}
inverse oflaplace (2s+6)/(s^2+4)	inverselaplace\:\frac{2s+6}{s^{2}+4}
x^4+5y^4sqrt(x^5+4)y^'=0	x^{4}+5y^{4}\sqrt{x^{5}+4}y^{\prime\:}=0
taylor (e^x)/(1-x)	taylor\:\frac{e^{x}}{1-x}
integral of (x^2+1)e^{-2x}	\int\:(x^{2}+1)e^{-2x}dx
integral of ((sec(x)tan(x))/(sec(x)-7))	\int\:(\frac{\sec(x)\tan(x)}{\sec(x)-7})dx
integral of 2/(3x^2)	\int\:\frac{2}{3x^{2}}dx
derivative of arctan(2x^2)	\frac{d}{dx}(\arctan(2x^{2}))
(\partial)/(\partial y)(y/(2x^2+y^2))	\frac{\partial\:}{\partial\:y}(\frac{y}{2x^{2}+y^{2}})
integral of (4x^3-3x+5)	\int\:(4x^{3}-3x+5)dx
integral of x(1+x^2)^{-1/2}	\int\:x(1+x^{2})^{-\frac{1}{2}}dx

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