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Popular Calculus Problems

integral of 7x(x^6-1/7)	\int\:7x(x^{6}-\frac{1}{7})dx
integral of x^{9/2}	\int\:x^{\frac{9}{2}}dx
(x-3)(dy)/(dx)=4(x-3)^4+y	(x-3)\frac{dy}{dx}=4(x-3)^{4}+y
(\partial)/(\partial y)(e^{yx^2})	\frac{\partial\:}{\partial\:y}(e^{yx^{2}})
integral of (70)/((x+1)(x^2+9)^2)	\int\:\frac{70}{(x+1)(x^{2}+9)^{2}}dx
limit as x approaches 1+of (x+7)/(x+2)	\lim\:_{x\to\:1+}(\frac{x+7}{x+2})
derivative of x-ln(x)	derivative\:x-\ln(x)
implicit (dy)/(dx),y=2x	implicit\:\frac{dy}{dx},y=2x
area 7x, 1/2 x,18-x^2	area\:7x,\frac{1}{2}x,18-x^{2}
integral of (4x+7)/(x^2+1)	\int\:\frac{4x+7}{x^{2}+1}dx
integral of e^{-2x}sin(3x)	\int\:e^{-2x}\sin(3x)dx
derivative of f(x)=x^2sin(2x)	derivative\:f(x)=x^{2}\sin(2x)
integral of 1/(-2x^2-x+1)	\int\:\frac{1}{-2x^{2}-x+1}dx
y^{''}-y^'=1	y^{\prime\:\prime\:}-y^{\prime\:}=1
integral of (4^x+10^x)/(2^x)	\int\:\frac{4^{x}+10^{x}}{2^{x}}dx
integral of 1/(x(1+sqrt(x)))	\int\:\frac{1}{x(1+\sqrt{x})}dx
integral of (sqrt(x))/2 (x-1)^2	\int\:\frac{\sqrt{x}}{2}(x-1)^{2}dx
derivative of cos^3(sqrt(x^2-1))	\frac{d}{dx}(\cos^{3}(\sqrt{x^{2}-1}))
limit as x approaches+0+of x^{2/x}	\lim\:_{x\to\:+0+}(x^{\frac{2}{x}})
y^{''}+15y^'+54y=0	y^{\prime\:\prime\:}+15y^{\prime\:}+54y=0
f(x)=(x+2)^{2/3}	f(x)=(x+2)^{\frac{2}{3}}
integral of 1/2 (1+cos(2x))	\int\:\frac{1}{2}(1+\cos(2x))dx
limit as x approaches 0+of (sin(2pi))/x	\lim\:_{x\to\:0+}(\frac{\sin(2π)}{x})
y^'=-4y,y(0)=8	y^{\prime\:}=-4y,y(0)=8
limit as x approaches 1 of 1/x-1/(e^x-1)	\lim\:_{x\to\:1}(\frac{1}{x}-\frac{1}{e^{x}-1})
derivative of ln(x+sqrt(x^2-1))	derivative\:\ln(x+\sqrt{x^{2}-1})
(\partial)/(\partial x)(e^{x+y}(x^2-y^2))	\frac{\partial\:}{\partial\:x}(e^{x+y}(x^{2}-y^{2}))
integral from 0 to 1 of (x^2+sqrt(x))	\int\:_{0}^{1}(x^{2}+\sqrt{x})dx
integral from-1 to 2 of 3xsqrt(3x^2+2)	\int\:_{-1}^{2}3x\sqrt{3x^{2}+2}dx
integral of 10	\int\:10dx
limit as x approaches 2+of x	\lim\:_{x\to\:2+}(x)
integral of (21)/(1-cos(7x))	\int\:\frac{21}{1-\cos(7x)}dx
sum from n=1 to infinity of 1/((2n-1)!)	\sum\:_{n=1}^{\infty\:}\frac{1}{(2n-1)!}
y^{''}+2y^'-y=0	y^{\prime\:\prime\:}+2y^{\prime\:}-y=0
derivative of (t-sqrt(t))/(t^{1/8)}	derivative\:\frac{t-\sqrt{t}}{t^{\frac{1}{8}}}
laplacetransform (5e^{2t}-3)^2	laplacetransform\:(5e^{2t}-3)^{2}
limit as x approaches 6 of 7x-6	\lim\:_{x\to\:6}(7x-6)
y^{''}+y=2tcos(t)	y^{\prime\:\prime\:}+y=2t\cos(t)
derivative of y=(4x^2+5x)^2	derivative\:y=(4x^{2}+5x)^{2}
integral of 2t^2e^{-st}	\int\:2t^{2}e^{-st}dt
tangent of f(x)=2x^3-4x+6,\at x=1	tangent\:f(x)=2x^{3}-4x+6,\at\:x=1
integral from 2 to 7 of g(x)	\int\:_{2}^{7}g(x)dx
derivative of (x^2-1/(3x))	\frac{d}{dx}(\frac{x^{2}-1}{3x})
integral of e^{-at}	\int\:e^{-at}dt
(dy)/(dx)=(x+y)/(x+y+1)	\frac{dy}{dx}=\frac{x+y}{x+y+1}
limit as x approaches infinity of 1.3x	\lim\:_{x\to\:\infty\:}(1.3x)
integral of 7sin(8x)cos(5x)	\int\:7\sin(8x)\cos(5x)dx
inverse oflaplace 2/s-1/(s^3)	inverselaplace\:\frac{2}{s}-\frac{1}{s^{3}}
taylor sin(pix),0.5	taylor\:\sin(πx),0.5
derivative of y=x^{cos(x)}	derivative\:y=x^{\cos(x)}
limit as x approaches infinity of 2x-5	\lim\:_{x\to\:\infty\:}(2x-5)
integral of 37arctan(sqrt(x))	\int\:37\arctan(\sqrt{x})dx
integral of 1/(7x)	\int\:\frac{1}{7x}dx
derivative of (-x^2-3^2sqrt(x^2+1))	\frac{d}{dx}((-x^{2}-3)^{2}\sqrt{x^{2}+1})
integral of (x-1/x)^2x	\int\:(x-\frac{1}{x})^{2}xdx
derivative of tan(11x)	\frac{d}{dx}(\tan(11x))
integral of 1/(\|x\|sqrt(x^2-1))	\int\:\frac{1}{\left\|x\right\|\sqrt{x^{2}-1}}dx
integral of x/(x^2+1)-3/(3x+1)	\int\:\frac{x}{x^{2}+1}-\frac{3}{3x+1}dx
f(y)=3y^2	f(y)=3y^{2}
derivative of 2x^3-3x^2-72x+15	\frac{d}{dx}(2x^{3}-3x^{2}-72x+15)
derivative of 1/4 ln(cos(4x))	\frac{d}{dx}(\frac{1}{4}\ln(\cos(4x)))
integral of 1/(1+e^x)	\int\:\frac{1}{1+e^{x}}dx
area-x^2+10x-16,2x-4	area\:-x^{2}+10x-16,2x-4
integral of 1/(x^{7/2)}	\int\:\frac{1}{x^{\frac{7}{2}}}dx
derivative of (f(x(4x))^2+5)	\frac{d}{dx}((f(x)(4x))^{2}+5)
area 6x+y^2=16,x=y	area\:6x+y^{2}=16,x=y
derivative of 3ax^4-4ax^3-5bx^2+7cx	\frac{d}{dx}(3ax^{4}-4ax^{3}-5bx^{2}+7cx)
integral of (1/(x^{-3)}+x^2e^{3x^3}-8/x)	\int\:(\frac{1}{x^{-3}}+x^{2}e^{3x^{3}}-\frac{8}{x})dx
y^'+6y=e^{-t}-6	y^{\prime\:}+6y=e^{-t}-6
integral of e^{4x}-5sin(x)	\int\:e^{4x}-5\sin(x)dx
tangent of f(x)= 8/(x^2+4)	tangent\:f(x)=\frac{8}{x^{2}+4}
integral of 3x^3+4x^2-5x	\int\:3x^{3}+4x^{2}-5xdx
limit as x approaches 0 of (2(y+x)-2y)/x	\lim\:_{x\to\:0}(\frac{2(y+x)-2y}{x})
integral of 6x^2+4x-1	\int\:6x^{2}+4x-1dx
integral of (10x^3-5x)/(sqrt(x^4-x^2+6))	\int\:\frac{10x^{3}-5x}{\sqrt{x^{4}-x^{2}+6}}dx
integral of 3x*e^x	\int\:3x\cdot\:e^{x}dx
integral of ((e^x))/(sqrt(1-e^{2x))}	\int\:\frac{(e^{x})}{\sqrt{1-e^{2x}}}dx
integral from-4 to 0 of (y/4+sqrt(y+5))	\int\:_{-4}^{0}(\frac{y}{4}+\sqrt{y+5})dy
integral of sin^2(3x)cos^2(3x)	\int\:\sin^{2}(3x)\cos^{2}(3x)dx
((2x^2+16x+x^{3^{1/2}}+5))/(x^3)	\frac{(2x^{2}+16x+x^{3^{\frac{1}{2}}}+5)}{x^{3}}
(d^2y)/(dx^2)-2a(dy)/(dx)+a^2y=0	\frac{d^{2}y}{dx^{2}}-2a\frac{dy}{dx}+a^{2}y=0
tangent of y=x^4+9x^2-x,(1,9)	tangent\:y=x^{4}+9x^{2}-x,(1,9)
integral from 1 to e of (ln(z))/(z^2)	\int\:_{1}^{e}\frac{\ln(z)}{z^{2}}dz
derivative of (80/(1+0.32x))	\frac{d}{dx}(\frac{80}{1+0.32x})
limit as x approaches 1 of e^{x-1}	\lim\:_{x\to\:1}(e^{x-1})
derivative of-2/(2x+5)	\frac{d}{dx}(-\frac{2}{2x+5})
derivative of f(x)=ln(4x^2+1)	derivative\:f(x)=\ln(4x^{2}+1)
limit as x approaches 1-of (2x)/(x^2-1)	\lim\:_{x\to\:1-}(\frac{2x}{x^{2}-1})
(\partial)/(\partial y)(x^2y+x+1)	\frac{\partial\:}{\partial\:y}(x^{2}y+x+1)
derivative of 2^{30}	derivative\:2^{30}
integral of sin(x/4)	\int\:\sin(\frac{x}{4})dx
integral of (x^3)/((x^4+3)^{(7/2))}	\int\:\frac{x^{3}}{(x^{4}+3)^{(\frac{7}{2})}}dx
integral of 1/((2+x)^2)	\int\:\frac{1}{(2+x)^{2}}dx
integral from 0 to infinity of e^{-ax}	\int\:_{0}^{\infty\:}e^{-ax}dx
derivative of ln(2x^2y)	\frac{d}{dx}(\ln(2x^{2}y))
integral of (x^2+4)	\int\:(x^{2}+4)dx
derivative of (x-1/(x^2-3x+3))	\frac{d}{dx}(\frac{x-1}{x^{2}-3x+3})
integral of 1/((100+x^2)^2)	\int\:\frac{1}{(100+x^{2})^{2}}dx
derivative of 3x(x^2-2/x)	\frac{d}{dx}(3x(x^{2}-\frac{2}{x}))
derivative of f(x)=\sqrt[6]{x^5}	derivative\:f(x)=\sqrt[6]{x^{5}}

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