Evaluate the indefinite integral. ∫3x+25x6dx

Question

Evaluate the indefinite integral.  ∫3x+25x6dx

censoratojk · Accepted Answer

Step 1
This question is based on indefinite integral.
General form,
Integral of

x^{n}

is

\frac{x^{(x + 1)}}{n + 1}

As for x = 1 formula violates because result comes is not defined.
Therefore, integral of 1/x is

\ln (x)

Step 2
Given

\int (\frac{3}{x} + \frac{2}{5 x^{6}}) d x

= \int \frac{3}{x} d x + \int \frac{2}{5 x^{6}} d x ∵ \int x^{n} d x = \frac{x^{n + 1}}{n + 1}

and

\int \frac{1}{x} d x = \ln (x)

= 3 \ln (x) + \frac{2}{5} \frac{x^{(- 6 + 1)}}{(- 6 + 1)} + C

= 3 \ln (x) + \frac{2}{5} \frac{x^{- 5}}{- 5} + C

= 3 \ln (x) - \frac{2}{25} x^{- 5} + C

Hence, Answer is

3 \ln (x) - \frac{2}{25} x^{- 5} + C

Foreckije · Accepted Answer

∫(3x+25⋅x6)dx  Lets

karton · Accepted Answer

Given: ∫3x+25x6dx Use properties of integrals ∫3xdx+∫25x6dx Evaluate the integrals 3ln⁡(|x|)−225x5 Add C Answer: 3ln⁡(|x|)−225x5+C

Answered question