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Popular Calculus Problems

integral from 2 to e^4 of 1/x	\int\:_{2}^{e^{4}}\frac{1}{x}dx
inverse oflaplace 4/(s^4)	inverselaplace\:\frac{4}{s^{4}}
integral of x^7e^{3x^4}	\int\:x^{7}e^{3x^{4}}dx
derivative of (t-sqrt(t))/(t^{1/9)}	derivative\:\frac{t-\sqrt{t}}{t^{\frac{1}{9}}}
derivative of 2x^4-6x^3-12x-8	\frac{d}{dx}(2x^{4}-6x^{3}-12x-8)
sum from n=5 to infinity of 1/(n(n-1))	\sum\:_{n=5}^{\infty\:}\frac{1}{n(n-1)}
integral from 2 to 4 of (x^4-1)	\int\:_{2}^{4}(x^{4}-1)dx
limit as x approaches 0 of (1+4x)^{6/x}	\lim\:_{x\to\:0}((1+4x)^{\frac{6}{x}})
(\partial)/(\partial y)(3x^2y+5xy^3)	\frac{\partial\:}{\partial\:y}(3x^{2}y+5xy^{3})
derivative of ((3-x))/(4x)	derivative\:\frac{(3-x)}{4x}
integral of cos^4(3-x)sin(3-x)	\int\:\cos^{4}(3-x)\sin(3-x)dx
area y=x,y=1-x^2,-1,2	area\:y=x,y=1-x^{2},-1,2
tangent of-(39)/((8x+5)^2),\at x=2	tangent\:-\frac{39}{(8x+5)^{2}},\at\:x=2
integral from 0 to 4 of (12)/(x^2+5x+6)	\int\:_{0}^{4}\frac{12}{x^{2}+5x+6}dx
integral of 4/(x^2+8x)	\int\:\frac{4}{x^{2}+8x}dx
integral from-1 to 1 of (3x)/((x+6)^2)	\int\:_{-1}^{1}\frac{3x}{(x+6)^{2}}dx
integral of 4xy	\int\:4xydx
derivative of e^{sqrt(x)}	derivative\:e^{\sqrt{x}}
integral of 3xsqrt(x)	\int\:3x\sqrt{x}dx
derivative of x-arctan(x)	\frac{d}{dx}(x-\arctan(x))
(\partial)/(\partial x)(ln(x^2+y))	\frac{\partial\:}{\partial\:x}(\ln(x^{2}+y))
integral of (2+u)/u	\int\:\frac{2+u}{u}du
derivative of y=x^3(3-x^2)	derivative\:y=x^{3}(3-x^{2})
(\partial)/(\partial x)(sin(pi(4x-2y)))	\frac{\partial\:}{\partial\:x}(\sin(π(4x-2y)))
slope of y=3x^2,\at x=1	slope\:y=3x^{2},\at\:x=1
integral of (sec^5(x))	\int\:(\sec^{5}(x))dx
slope ofintercept (-4,5),(5,-22)	slopeintercept\:(-4,5),(5,-22)
limit as x approaches 6 of pi	\lim\:_{x\to\:6}(π)
integral of (16x^3-32x^2+5)/(x^2-2x)	\int\:\frac{16x^{3}-32x^{2}+5}{x^{2}-2x}dx
integral of 8^{3x+5}	\int\:8^{3x+5}dx
inverse oflaplace 2/((s^2+4)^2)	inverselaplace\:\frac{2}{(s^{2}+4)^{2}}
parity xcsc(x)	parity\:x\csc(x)
(\partial)/(\partial y)(-arctan(x/y))	\frac{\partial\:}{\partial\:y}(-\arctan(\frac{x}{y}))
integral of (e^x+1)	\int\:(e^{x}+1)dx
derivative of x^4+12x^2+42	\frac{d}{dx}(x^{4}+12x^{2}+42)
derivative of (6x/(2+x^2))	\frac{d}{dx}(\frac{6x}{2+x^{2}})
xy^'=2y+x^3	xy^{\prime\:}=2y+x^{3}
(\partial)/(\partial x)(k)	\frac{\partial\:}{\partial\:x}(k)
integral of 1/(ax^2+bx+c)	\int\:\frac{1}{ax^{2}+bx+c}dx
y^'-((2x)/(1+x^2))y=0,y(0)=4	y^{\prime\:}-(\frac{2x}{1+x^{2}})y=0,y(0)=4
derivative of (t^2-t)(t^2+t)	derivative\:(t^{2}-t)(t^{2}+t)
(\partial)/(\partial y)(e^{3xy})	\frac{\partial\:}{\partial\:y}(e^{3xy})
(dy)/(dx)+5y=0	\frac{dy}{dx}+5y=0
(\partial)/(\partial x)(5+e^{-xy}cos(y))	\frac{\partial\:}{\partial\:x}(5+e^{-xy}\cos(y))
limit as x approaches 7 of (x^2-5x-14)/(x-7)	\lim\:_{x\to\:7}(\frac{x^{2}-5x-14}{x-7})
integral from 1 to e of (x^2-1)/x	\int\:_{1}^{e}\frac{x^{2}-1}{x}dx
y^{''}-6y^'+6y=0	y^{\prime\:\prime\:}-6y^{\prime\:}+6y=0
(\partial)/(\partial x)(sin(x^2y))	\frac{\partial\:}{\partial\:x}(\sin(x^{2}y))
derivative of sin((pix^5))	\frac{d}{dx}(\sin((πx)^{5}))
slope of (7.3)(6.7)	slope\:(7.3)(6.7)
tangent of f(x)=(10x)/(x+4),\at x=4,y=5	tangent\:f(x)=\frac{10x}{x+4},\at\:x=4,y=5
derivative of 4x^4y^3+cos(x^2)	\frac{d}{dx}(4x^{4}y^{3}+\cos(x^{2}))
integral of x^{2n}	\int\:x^{2n}dx
derivative of (x^4/8)	\frac{d}{dx}(\frac{x^{4}}{8})
(\partial)/(\partial x)(e^{4(e^x-1)})	\frac{\partial\:}{\partial\:x}(e^{4(e^{x}-1)})
limit as x approaches 0 of (1-6x)^{6/x}	\lim\:_{x\to\:0}((1-6x)^{\frac{6}{x}})
(\partial)/(\partial y)(3x^4y^2+3)	\frac{\partial\:}{\partial\:y}(3x^{4}y^{2}+3)
y^3y^'+x^3=0	y^{3}y^{\prime\:}+x^{3}=0
tangent of x^2+2x	tangent\:x^{2}+2x
integral of (6x^2-8x+2)	\int\:(6x^{2}-8x+2)dx
y^{'''}+y^'=cot(x)	y^{\prime\:\prime\:\prime\:}+y^{\prime\:}=\cot(x)
y^{''}+5(dy)/(dx)+6y=2e^x	y^{\prime\:\prime\:}+5\frac{dy}{dx}+6y=2e^{x}
sum from n=1 to infinity of (9n)/(2n+1)	\sum\:_{n=1}^{\infty\:}\frac{9n}{2n+1}
f(x)= 1/(arctan(x^2))	f(x)=\frac{1}{\arctan(x^{2})}
derivative of 5arccot(t)+5arccot(1/t)	derivative\:5\arccot(t)+5\arccot(\frac{1}{t})
d/(dθ)(1+sin(θ))	\frac{d}{dθ}(1+\sin(θ))
integral of (e^y(1-e^{-2y}))/((e^y+e^{-y))}	\int\:\frac{e^{y}(1-e^{-2y})}{(e^{y}+e^{-y})}dy
integral of x/(2x^2+2x+7)	\int\:\frac{x}{2x^{2}+2x+7}dx
y^{''}+a^2y=sin(b*t)	y^{\prime\:\prime\:}+a^{2}y=\sin(b\cdot\:t)
integral of (6x^2-4x+2)(x^3-x^2+x+1)^7	\int\:(6x^{2}-4x+2)(x^{3}-x^{2}+x+1)^{7}dx
(\partial)/(\partial x)(sqrt(a^2-x^2-y^2))	\frac{\partial\:}{\partial\:x}(\sqrt{a^{2}-x^{2}-y^{2}})
integral of (e^{x^2})/x	\int\:\frac{e^{x^{2}}}{x}dx
limit as x approaches 3 of 5/(2x-6)	\lim\:_{x\to\:3}(\frac{5}{2x-6})
integral of (5-3x)e^{2x+3}	\int\:(5-3x)e^{2x+3}dx
integral of 1/(sqrt(x)(\sqrt{x)+1)^3}	\int\:\frac{1}{\sqrt{x}(\sqrt{x}+1)^{3}}dx
(\partial ^2)/(\partial {u)(w)\partial w}(e^{{u}(w)-w})	\frac{\partial\:^{2}}{\partial\:{u}(w)\partial\:w}(e^{{u}(w)-w})
integral of 1/((x-1)(x^2+9))	\int\:\frac{1}{(x-1)(x^{2}+9)}dx
integral of 1/(9-4x)	\int\:\frac{1}{9-4x}dx
derivative of y=(-12)/(\sqrt[4]{x)}	derivative\:y=\frac{-12}{\sqrt[4]{x}}
2x+y+(x+2y)y^'=0	2x+y+(x+2y)y^{\prime\:}=0
integral of-2x^2+6x	\int\:-2x^{2}+6xdx
derivative of (cos^2(s)-11s^2)^2	derivative\:(\cos^{2}(s)-11s^{2})^{2}
derivative of-3cot(xcsc(x))	\frac{d}{dx}(-3\cot(x)\csc(x))
derivative of (1+x^4tan(x)^{-5})	\frac{d}{dx}((1+x^{4}\tan(x))^{-5})
limit as x approaches 4+of (3+x)/(4-x)	\lim\:_{x\to\:4+}(\frac{3+x}{4-x})
derivative of f(x)=(3x^5)/5-(10x^4)/3	derivative\:f(x)=\frac{3x^{5}}{5}-\frac{10x^{4}}{3}
(dy}{dx}=\frac{3x^2)/y	\frac{dy}{dx}=\frac{3x^{2}}{y}
laplacetransform 2sin^2(t)	laplacetransform\:2\sin^{2}(t)
derivative of (x^2/((1+2tan(x))))	\frac{d}{dx}(\frac{x^{2}}{(1+2\tan(x))})
laplacetransform 4cos(3t)	laplacetransform\:4\cos(3t)
limit as x approaches 0 of 96	\lim\:_{x\to\:0}(96)
integral of 9te^t	\int\:9te^{t}dt
integral of 15xsqrt(x+1)	\int\:15x\sqrt{x+1}dx
sum from n=2 to infinity of 1/(n^3-n)	\sum\:_{n=2}^{\infty\:}\frac{1}{n^{3}-n}
integral of (x^2-3x-1)/(x(x^2+4))	\int\:\frac{x^{2}-3x-1}{x(x^{2}+4)}dx
derivative of x^{-2}	derivative\:x^{-2}
integral of 1-x^{-0.52}	\int\:1-x^{-0.52}dx
integral of x^3+5	\int\:x^{3}+5dx
integral of sin(4pix)sin(npix)	\int\:\sin(4πx)\sin(nπx)dx
derivative of log_{3}(8x-1)	\frac{d}{dx}(\log_{3}(8x-1))

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