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Popular Calculus Problems

integral from 0 to 5 of 20e^{0.02x}	\int\:_{0}^{5}20e^{0.02x}dx
derivative of f(x)=(x^3)/(12)+1/x	derivative\:f(x)=\frac{x^{3}}{12}+\frac{1}{x}
(\partial)/(\partial y)(zy^2(t+1))	\frac{\partial\:}{\partial\:y}(zy^{2}(t+1))
integral of e^{-sin(x)}cos(x)	\int\:e^{-\sin(x)}\cos(x)dx
limit as x approaches 0-of 1-3/x+1/(x^2)	\lim\:_{x\to\:0-}(1-\frac{3}{x}+\frac{1}{x^{2}})
derivative of y=(1+4x)^{3/2}	derivative\:y=(1+4x)^{\frac{3}{2}}
integral of xsin((npix)/3)	\int\:x\sin(\frac{nπx}{3})dx
inverse oflaplace 1/(s^2(s^2+1^2))	inverselaplace\:\frac{1}{s^{2}(s^{2}+1^{2})}
integral of x*arctan(x)	\int\:x\cdot\:\arctan(x)dx
derivative of x(1-4/(x+3))	derivative\:x(1-\frac{4}{x+3})
derivative of 2\sqrt[3]{x}-1	derivative\:2\sqrt[3]{x}-1
derivative of 2/(e^{x/2+e^{-x/2}})	\frac{d}{dx}(\frac{2}{e^{\frac{x}{2}}+e^{-\frac{x}{2}}})
f(x)=5tan(3x)	f(x)=5\tan(3x)
sum from n=1 to infinity of (n-5)/(n+2)	\sum\:_{n=1}^{\infty\:}\frac{n-5}{n+2}
f(x)= 1/(x^2)-x	f(x)=\frac{1}{x^{2}}-x
(\partial)/(\partial y)(xe^{-xy})	\frac{\partial\:}{\partial\:y}(xe^{-xy})
derivative of (4x/(e^x))	\frac{d}{dx}(\frac{4x}{e^{x}})
limit as x approaches 0 of (1cos(3x))/x	\lim\:_{x\to\:0}(\frac{1\cos(3x)}{x})
derivative of (3x)/2	derivative\:\frac{3x}{2}
derivative of 7e^2	derivative\:7e^{2}
(\partial)/(\partial x)(yz^2)	\frac{\partial\:}{\partial\:x}(yz^{2})
integral of x^2-9x+4	\int\:x^{2}-9x+4dx
derivative of sqrt(1/(cos(x)))	derivative\:\sqrt{\frac{1}{\cos(x)}}
integral of (e^{8sqrt(t)})/(sqrt(t))	\int\:\frac{e^{8\sqrt{t}}}{\sqrt{t}}dt
inverse oflaplace 1/(s^2+0.5s+1)	inverselaplace\:\frac{1}{s^{2}+0.5s+1}
limit as x approaches 1 of (x-1)^{ln(x)}	\lim\:_{x\to\:1}((x-1)^{\ln(x)})
(dy)/(dx)=-10xy	\frac{dy}{dx}=-10xy
integral of tsin(t)cos(t)	\int\:t\sin(t)\cos(t)dt
limit as x approaches infinity of xy	\lim\:_{x\to\:\infty\:}(xy)
(dy)/(dx)+y/x =4x^8y^2	\frac{dy}{dx}+\frac{y}{x}=4x^{8}y^{2}
(\partial)/(\partial x)(-x^4)	\frac{\partial\:}{\partial\:x}(-x^{4})
x^2y^{''}+3xy^'+y=0,y(1)=3.6,y^'(1)=0.4	x^{2}y^{\prime\:\prime\:}+3xy^{\prime\:}+y=0,y(1)=3.6,y^{\prime\:}(1)=0.4
integral from-1 to 7 of 3x+7	\int\:_{-1}^{7}3x+7dx
(\partial)/(\partial x)((x-4)ln(xy))	\frac{\partial\:}{\partial\:x}((x-4)\ln(xy))
integral of-xcos(x)+x	\int\:-x\cos(x)+xdx
integral from 0 to l of cos((piy)/(2l))	\int\:_{0}^{l}\cos(\frac{πy}{2l})dy
derivative of g(t)=t-4/(t^3)	derivative\:g(t)=t-\frac{4}{t^{3}}
f(t)=2e^{2t}	f(t)=2e^{2t}
derivative of (x+1/2)	\frac{d}{dx}(\frac{x+1}{2})
integral of 1/(x^2+2x+2)	\int\:\frac{1}{x^{2}+2x+2}dx
integral of (4x^5-x^3-5x)	\int\:(4x^{5}-x^{3}-5x)dx
integral of-8x^7y^{-5}+6x^6y^{-4}	\int\:-8x^{7}y^{-5}+6x^{6}y^{-4}dy
integral of (ln(x))^{10} 1/x	\int\:(\ln(x))^{10}\frac{1}{x}dx
y^{'''}-y^{''}+8y^'-8y=0	y^{\prime\:\prime\:\prime\:}-y^{\prime\:\prime\:}+8y^{\prime\:}-8y=0
derivative of 25xe^{-x}	derivative\:25xe^{-x}
(d^3)/(dx^3)(2^x)	\frac{d^{3}}{dx^{3}}(2^{x})
(\partial)/(\partial x)(6xy^4z^3)	\frac{\partial\:}{\partial\:x}(6xy^{4}z^{3})
integral of (-2)/((x^2+2)^{3/2)}	\int\:\frac{-2}{(x^{2}+2)^{\frac{3}{2}}}dx
integral of-9tan^2(x)	\int\:-9\tan^{2}(x)dx
tangent of f(x)=sqrt(x),\at x=16	tangent\:f(x)=\sqrt{x},\at\:x=16
derivative of 1/(sqrt(1+x^{12)})	\frac{d}{dx}(\frac{1}{\sqrt{1+x^{12}}})
derivative of 2x+5x^{-1}	derivative\:2x+5x^{-1}
integral from 1 to 4 of (4x^2-2x)	\int\:_{1}^{4}(4x^{2}-2x)dx
((3y^2-x^2)/(y^5))(dy)/(dx)+x/(2y^4)=0	(\frac{3y^{2}-x^{2}}{y^{5}})\frac{dy}{dx}+\frac{x}{2y^{4}}=0
(\partial)/(\partial x)(x(x^2+1))	\frac{\partial\:}{\partial\:x}(x(x^{2}+1))
inverse oflaplace 3/(s-5)-2/(s+7)	inverselaplace\:\frac{3}{s-5}-\frac{2}{s+7}
integral of b^x	\int\:b^{x}dx
(dy)/(dx)=((x^2+1))/(e^y)	\frac{dy}{dx}=\frac{(x^{2}+1)}{e^{y}}
integral of ((x^2)/(sqrt(1-x^2)))	\int\:(\frac{x^{2}}{\sqrt{1-x^{2}}})dx
laplacetransform 2tcos(t)	laplacetransform\:2t\cos(t)
-ydx+(x+xy)dy=0	-ydx+(x+xy)dy=0
limit as x approaches-8+of (x+9)/(x+8)	\lim\:_{x\to\:-8+}(\frac{x+9}{x+8})
tangent of f(x)=x^2-2x,\at x=-2	tangent\:f(x)=x^{2}-2x,\at\:x=-2
integral of 1/(t^5)	\int\:\frac{1}{t^{5}}dt
tangent of f(x)=x^4+6x^2-x,(1,6)	tangent\:f(x)=x^{4}+6x^{2}-x,(1,6)
derivative of 3/(x^7)	derivative\:\frac{3}{x^{7}}
2xy^'+7y=7x^4,y(1)=4	2xy^{\prime\:}+7y=7x^{4},y(1)=4
integral of ((1+x))/((1+x^2))	\int\:\frac{(1+x)}{(1+x^{2})}dx
integral from-2 to 2 of (x^3cos(x/2)+1/2)sqrt(4-x^2)	\int\:_{-2}^{2}(x^{3}\cos(\frac{x}{2})+\frac{1}{2})\sqrt{4-x^{2}}dx
sum from n=1 to infinity of 1/(n^2+4n+5)	\sum\:_{n=1}^{\infty\:}\frac{1}{n^{2}+4n+5}
integral from 7 to 2 of g(x)	\int\:_{7}^{2}g(x)dx
derivative of cos(2x-2xsin(2x))	\frac{d}{dx}(\cos(2x)-2x\sin(2x))
integral of (22x+88)/(2x^2+9x-5)	\int\:\frac{22x+88}{2x^{2}+9x-5}dx
integral of u^{-3/2}	\int\:u^{-\frac{3}{2}}du
derivative of y=csc^2(x)	derivative\:y=\csc^{2}(x)
integral of x(x+5)	\int\:x(x+5)dx
(\partial)/(\partial x)(sqrt(2x+y^2))	\frac{\partial\:}{\partial\:x}(\sqrt{2x+y^{2}})
inverse oflaplace (10)/s (1/(10s+1))	inverselaplace\:\frac{10}{s}(\frac{1}{10s+1})
derivative of x^2+e^x	derivative\:x^{2}+e^{x}
derivative of (x^2+x(x^2-x))	\frac{d}{dx}((x^{2}+x)(x^{2}-x))
(\partial)/(\partial x)((x-y)/(x+2y))	\frac{\partial\:}{\partial\:x}(\frac{x-y}{x+2y})
derivative of (sin(1/x)/(x^2))	\frac{d}{dx}(\frac{\sin(\frac{1}{x})}{x^{2}})
limit as x approaches-infinity of 9	\lim\:_{x\to\:-\infty\:}(9)
integral of (4-3x)^5	\int\:(4-3x)^{5}dx
inverse oflaplace 4/(5s+1)	inverselaplace\:\frac{4}{5s+1}
integral of ln\|1+x\|	\int\:\ln\left\|1+x\right\|dx
(dy)/(dx)=e^{-x}	\frac{dy}{dx}=e^{-x}
integral of-(1400)/(x^2)	\int\:-\frac{1400}{x^{2}}dx
limit as x approaches-1+of 6x^2+11	\lim\:_{x\to\:-1+}(6x^{2}+11)
integral of cos^7(1/5 x)	\int\:\cos^{7}(\frac{1}{5}x)dx
integral of t^2e^{-10t}	\int\:t^{2}e^{-10t}dt
(\partial)/(\partial x)(-6xysin(xy^2))	\frac{\partial\:}{\partial\:x}(-6xy\sin(xy^{2}))
area \sqrt[3]{x}, 1/x ,8,1	area\:\sqrt[3]{x},\frac{1}{x},8,1
integral of x^3sqrt(ax^4-b)	\int\:x^{3}\sqrt{ax^{4}-b}dx
derivative of 1/((x^2-1)(x^2+x+1))	derivative\:\frac{1}{(x^{2}-1)(x^{2}+x+1)}
taylor e^{-x^2}1	taylor\:e^{-x^{2}}1
integral of sin(x)+x	\int\:\sin(x)+xdx
integral of (36)/x	\int\:\frac{36}{x}dx
integral of 18x^5	\int\:18x^{5}dx
(d^4)/(dx^4)(17e^{x^2})	\frac{d^{4}}{dx^{4}}(17e^{x^{2}})

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