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Popular Calculus Problems

integral of 1/(e^{5x)}	\int\:\frac{1}{e^{5x}}dx
integral of-7x^{-8}	\int\:-7x^{-8}dx
derivative of y=5csc(x)+7cos(x)	derivative\:y=5\csc(x)+7\cos(x)
integral of (x^2-10x+4)/(x^3)	\int\:\frac{x^{2}-10x+4}{x^{3}}dx
derivative of 2-e^{-x}	\frac{d}{dx}(2-e^{-x})
sum from n=0 to infinity of 1/(2^{2n+1)}	\sum\:_{n=0}^{\infty\:}\frac{1}{2^{2n+1}}
limit as x approaches infinity of 1	\lim\:_{x\to\:\infty\:}(1)
integral of (2t)/(t^2+1)	\int\:\frac{2t}{t^{2}+1}dt
derivative of f(x)=\|2x-3\|	derivative\:f(x)=\left\|2x-3\right\|
f(x)=-sin(x^2)*2x	f(x)=-\sin(x^{2})\cdot\:2x
integral of (x^4-3x^2+x-sqrt(x)+2)/x	\int\:\frac{x^{4}-3x^{2}+x-\sqrt{x}+2}{x}dx
laplacetransform 7+3t	laplacetransform\:7+3t
integral of (x^3)/((1-2x^4)^5)	\int\:\frac{x^{3}}{(1-2x^{4})^{5}}dx
xy^{''}=y^'+(y^')^3	xy^{\prime\:\prime\:}=y^{\prime\:}+(y^{\prime\:})^{3}
limit as x approaches-3-of (4x)/(9-x^2)	\lim\:_{x\to\:-3-}(\frac{4x}{9-x^{2}})
integral of 1/(x^2-x+2)	\int\:\frac{1}{x^{2}-x+2}dx
integral of 1/(x^2(x^2-1))	\int\:\frac{1}{x^{2}(x^{2}-1)}dx
(t^2+16)^2y^'+2t(t^2+16)y=4,y(-2)=10	(t^{2}+16)^{2}y^{\prime\:}+2t(t^{2}+16)y=4,y(-2)=10
integral of ((arctan(x))/(1+x^2))	\int\:(\frac{\arctan(x)}{1+x^{2}})dx
integral of sqrt(36-4x^2)	\int\:\sqrt{36-4x^{2}}dx
integral of 3xe^{-3x}	\int\:3xe^{-3x}dx
area y=x^2-2x,y=3x+6	area\:y=x^{2}-2x,y=3x+6
integral of e^{-x}sin(4x)	\int\:e^{-x}\sin(4x)dx
(x^2+1)y^'+6x(y-1)=0,y(0)=8	(x^{2}+1)y^{\prime\:}+6x(y-1)=0,y(0)=8
integral of (ln(y))^2	\int\:(\ln(y))^{2}dy
area (x^2-1)(x^2-4),x=0,x=5	area\:(x^{2}-1)(x^{2}-4),x=0,x=5
area xsqrt(4-x^2),0	area\:x\sqrt{4-x^{2}},0
simplify sqrt(x)+sqrt(y)	simplify\:\sqrt{x}+\sqrt{y}
derivative of 4x(x^2+1)	\frac{d}{dx}(4x(x^{2}+1))
area y= 1/x ,x=2,y=-1	area\:y=\frac{1}{x},x=2,y=-1
integral from-infinity to-1 of xe^x	\int\:_{-\infty\:}^{-1}xe^{x}dx
limit as x approaches 6 of 9x+x^2(3x+5)	\lim\:_{x\to\:6}(9x+x^{2}(3x+5))
derivative of y=(2x-1)(3x+4)(x+7)	derivative\:y=(2x-1)(3x+4)(x+7)
integral of sqrt(t)-8cos(t)	\int\:\sqrt{t}-8\cos(t)dt
integral of (x^3-x^2-2x)/(4x-2)	\int\:\frac{x^{3}-x^{2}-2x}{4x-2}dx
limit as x approaches infinity+of (log_{6}(x))/(log_{8)(x)}	\lim\:_{x\to\:\infty\:+}(\frac{\log_{6}(x)}{\log_{8}(x)})
(d^5)/(dx^5)(1/x+cos(2x))	\frac{d^{5}}{dx^{5}}(\frac{1}{x}+\cos(2x))
derivative of 12xy	\frac{d}{dx}(12xy)
derivative of f(x)=(sqrt(x)+x)/(x^2)	derivative\:f(x)=\frac{\sqrt{x}+x}{x^{2}}
derivative of f(x)=e^{(x^2-x)}	derivative\:f(x)=e^{(x^{2}-x)}
integral of e^x-xe^{x^2}	\int\:e^{x}-xe^{x^{2}}dx
integral of 1/(sqrt(6+4x-2x^2))	\int\:\frac{1}{\sqrt{6+4x-2x^{2}}}dx
derivative of ln(81sin^2(x))	derivative\:\ln(81\sin^{2}(x))
integral of (200)/(20-3x)	\int\:\frac{200}{20-3x}dx
limit as x approaches 1 of x^3+1	\lim\:_{x\to\:1}(x^{3}+1)
limit as x approaches infinity of 5*x	\lim\:_{x\to\:\infty\:}(5\cdot\:x)
integral of 1/((1+x)sqrt(x))	\int\:\frac{1}{(1+x)\sqrt{x}}dx
derivative of \sqrt[3]{x}-4/x	\frac{d}{dx}(\sqrt[3]{x}-\frac{4}{x})
integral from 0 to 1 of 4e^{6sqrt(x)}	\int\:_{0}^{1}4e^{6\sqrt{x}}dx
sum from n=0 to infinity of (3^n)/(n!)	\sum\:_{n=0}^{\infty\:}\frac{3^{n}}{n!}
derivative of (xcos(x)sin(x))	\frac{d}{dx}((x)\cos(x)\sin(x))
(\partial)/(\partial x)(e^{2(2x+y)})	\frac{\partial\:}{\partial\:x}(e^{2(2x+y)})
derivative of ln(x^2-1)	derivative\:\ln(x^{2}-1)
sum from n=0 to infinity of nx^{n-1}	\sum\:_{n=0}^{\infty\:}nx^{n-1}
derivative of x^{(-5/9})	\frac{d}{dx}(x^{\frac{-5}{9}})
derivative of f(x)=e^{-(x^2)/2}	derivative\:f(x)=e^{-\frac{x^{2}}{2}}
integral from 2 to 8 of (-x+10)	\int\:_{2}^{8}(-x+10)dx
sqrt(y)dx+(1+x)dy=0,y(0)=1	\sqrt{y}dx+(1+x)dy=0,y(0)=1
integral of (7/(x^5)+8e^{2x}-4x)	\int\:(\frac{7}{x^{5}}+8e^{2x}-4x)dx
sum from n=1 to infinity of (-2^n)/(n^7)	\sum\:_{n=1}^{\infty\:}\frac{-2^{n}}{n^{7}}
derivative of (12-3y-2x/4)	\frac{d}{dx}(\frac{12-3y-2x}{4})
derivative of y=sqrt(x)(x^2+1)^3	derivative\:y=\sqrt{x}(x^{2}+1)^{3}
integral of (cos(nx))	\int\:(\cos(nx))dx
integral from-1 to 2 of (1-x)	\int\:_{-1}^{2}(1-x)dx
sum from n=1 to infinity of 1/(3^n)	\sum\:_{n=1}^{\infty\:}\frac{1}{3^{n}}
integral of tan(5θ)	\int\:\tan(5θ)dθ
integral of (3/2)^x	\int\:(\frac{3}{2})^{x}dx
derivative of 3x^7-7x^3+21x^2	\frac{d}{dx}(3x^{7}-7x^{3}+21x^{2})
integral of 9sec^4(x)	\int\:9\sec^{4}(x)dx
derivative of 5x^4-3x^2+1/(sqrt(x)-7)	\frac{d}{dx}(5x^{4}-3x^{2}+\frac{1}{\sqrt{x}}-7)
integral of 1/(3+3cos(x))	\int\:\frac{1}{3+3\cos(x)}dx
(\partial)/(\partial x)(ln(xcos(y)))	\frac{\partial\:}{\partial\:x}(\ln(x\cos(y)))
derivative of 5/(\sqrt[5]{t)}+5t	derivative\:\frac{5}{\sqrt[5]{t}}+5t
integral of 3t^2sin(t^3)	\int\:3t^{2}\sin(t^{3})dt
derivative of (x^3)	\frac{d}{dx}((x)^{3})
integral from 1 to 2 of 8r^4ln(r)	\int\:_{1}^{2}8r^{4}\ln(r)dr
y^{'''}+y^{''}-2=0	y^{\prime\:\prime\:\prime\:}+y^{\prime\:\prime\:}-2=0
integral of (x^2+2x+2)/(x+1)	\int\:\frac{x^{2}+2x+2}{x+1}dx
derivative of sec^2(x/a+csc^2(x/a))	\frac{d}{dx}(\sec^{2}(\frac{x}{a})+\csc^{2}(\frac{x}{a}))
tangent of f(x)=x^2-6,(2,-2)	tangent\:f(x)=x^{2}-6,(2,-2)
limit as x approaches-infinity of 2.3^x	\lim\:_{x\to\:-\infty\:}(2.3^{x})
2y^{''}+35y=0	2y^{\prime\:\prime\:}+35y=0
limit as x approaches 2 of (x^2)/(x^2+1)	\lim\:_{x\to\:2}(\frac{x^{2}}{x^{2}+1})
integral of e^{-inx}	\int\:e^{-inx}dx
integral of (sin(x)-cos(x))	\int\:(\sin(x)-\cos(x))dx
integral of x^2cos(n)x	\int\:x^{2}\cos(n)xdx
limit as x approaches 6 of-2x-5	\lim\:_{x\to\:6}(-2x-5)
laplacetransform f(t)=(e^t-e^{-t})^2	laplacetransform\:f(t)=(e^{t}-e^{-t})^{2}
y^'+8y=3x	y^{\prime\:}+8y=3x
(\partial)/(\partial u)(2uv)	\frac{\partial\:}{\partial\:u}(2uv)
derivative of (x-2)(3x+1)^2	derivative\:(x-2)(3x+1)^{2}
(dy)/(dx)=e^{6x}+9y	\frac{dy}{dx}=e^{6x}+9y
area 5x-x^2,x,4,4	area\:5x-x^{2},x,4,4
integral of cos^3(y)	\int\:\cos^{3}(y)dy
(\partial)/(\partial x)(x^2e^{sqrt(2xy)})	\frac{\partial\:}{\partial\:x}(x^{2}e^{\sqrt{2xy}})
y^'-3y=e^{2t}	y^{\prime\:}-3y=e^{2t}
maclaurin 1-(1-x)^{sqrt(2)-1}	maclaurin\:1-(1-x)^{\sqrt{2}-1}
taylor ln(1-4x)	taylor\:\ln(1-4x)
integral of e^{t^2-t}	\int\:e^{t^{2}-t}dt
(\partial)/(\partial x)(ln(5x+3y))	\frac{\partial\:}{\partial\:x}(\ln(5x+3y))

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