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Popular >

integral of 2^t(1+5^t)

Solution

\int 2^{t} (1 + 5^{t}) d t

Solution

\frac{2 ^{t}}{ln ( 2 )} + \frac{1 0 ^{t}}{ln ( 10 )} + C

Solution steps

\int 2^{t} (1 + 5^{t}) d t

Expand

2^{t} (1 + 5^{t}) : 2^{t} + 1 0^{t}

= \int 2^{t} + 1 0^{t} d t

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 2^{t} d t + \int 1 0^{t} d t

\int 2^{t} d t = \frac{2 ^{t}}{ln ( 2 )}

\int 1 0^{t} d t = \frac{1 0 ^{t}}{ln ( 10 )}

= \frac{2 ^{t}}{ln ( 2 )} + \frac{1 0 ^{t}}{ln ( 10 )}

Add a constant to the solution

= \frac{2 ^{t}}{ln ( 2 )} + \frac{1 0 ^{t}}{ln ( 10 )} + C

Popular Examples

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\int \frac{1}{4 ^{x} + 1} d x

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\int 9 - r^{2} d r

integral of-x^4e^{x^5}

\int - x^{4} e^{x^{5}} d x

integral of (sqrt(9-x^2))^3

\int (9 - x^{2})^{3} d x

integral of cos^5(x/3)

\int cos^{5} (\frac{x}{3}) d x

Frequently Asked Questions (FAQ)

What is the integral of 2^t(1+5^t) ?
The integral of 2^t(1+5^t) is (2^t)/(ln(2))+(10^t)/(ln(10))+C